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• [From BIP141] If the version is 0:
  • If the program is not 20 or 32 bytes, fail.
  • If the program is 20 bytes hash:
    • Execute the script OP_DUP OP_HASH160 hash OP_EQUALVERIFY OP_CHECKSIG, with initial stack input. If execution aborts, fail.
    • If the resulting stack is not exactly one element, or that element has numerical value 0, fail.
  • If the program is 32 bytes hash:
    • If input is empty, or its top element's SHA256 hash does not equal hash, fail.
    • Execute the top element of input as script, with the other elements as input. If execution aborts, fail.
    • If the resulting stack is not exactly one element, or that element has numerical value 0, fail.
• [From BIP341] If the version is 1, the program length is 32, and this is not operating inside a P2SH wrapping:
  • If the input consists of 0 elements, fail.
  • If the last element of input starts with byte 0x50, call it the annex and remove it from the input.
  • If the (remainder of) input consists of a single element, evaluate it as a Taproot key path spend:
    • The element is interpreted as a single BIP340 (Schnorr) signature for the transaction, using a message hashing scheme described in BIP341. If the signature is invalid, fail.
  • If the (remainder of) input consists of two or more elements, evaluate it as a Taproot script path spend:
    • The last element of input is interpreted as a Taproot control block, encoding a leaf_version, an internal x-only public key, and a Merkle path, and the penultimate element of input is called the taproot_script. The control block and taproot_script are removed from input.
      • Recompute the Merkle root of the script tree, starting from the leaf (leaf_version and taproot_script), and then tweak the internal x-only key with that Merkle root. If the result does not match the 32-byte witness program, fail.
      • [From BIP342] If the leaf_version is 0xc0, taproot_script is evaluated according to the Tapscript validation rules, with the remaining of input as initial stack. See BIP342 for how this differs from normal script execution.
• If no failure occurred up to this point, return success.

• [From BIP141] If the version is 0:
  • If the program is not 20 or 32 bytes, fail.
  • If the program is 20 bytes hash:
    • If input is not exactly 2 elements, fail.
    • Execute the script OP_DUP OP_HASH160 hash OP_EQUALVERIFY OP_CHECKSIG, with initial stack input. If execution aborts, fail.
    • If the resulting stack is not exactly one element, or that element has numerical value 0, fail.
  • If the program is 32 bytes hash:
    • If input is empty, or its top element's SHA256 hash does not equal hash, fail.
    • Execute the top element of input as script, with the other elements as input. If execution aborts, fail.
    • If the resulting stack is not exactly one element, or that element has numerical value 0, fail.
• [From BIP341] If the version is 1, the program length is 32, and this is not operating inside a P2SH wrapping:
  • If the input consists of 0 elements, fail.
  • If the last element of input starts with byte 0x50, call it the annex and remove it from the input.
  • If the (remainder of) input consists of a single element, evaluate it as a Taproot key path spend:
    • The element is interpreted as a single BIP340 (Schnorr) signature for the transaction, using a message hashing scheme described in BIP341. If the signature is invalid, fail.
  • If the (remainder of) input consists of two or more elements, evaluate it as a Taproot script path spend:
    • The last element of input is interpreted as a Taproot control block, encoding a leaf_version, an internal x-only public key, and a Merkle path, and the penultimate element of input is called the taproot_script. The control block and taproot_script are removed from input.
      • Recompute the Merkle root of the script tree, starting from the leaf (leaf_version and taproot_script), and then tweak the internal x-only key with that Merkle root. If the result does not match the 32-byte witness program, fail.
      • [From BIP342] If the leaf_version is 0xc0, taproot_script is evaluated according to the Tapscript validation rules, with the remaining of input as initial stack. See BIP342 for how this differs from normal script execution.
• If no failure occurred up to this point, return success.

• Execute the scriptSig, and call the resulting stack stack. If execution aborts, fail.
• Execute the scriptPubKey with stack as input, and call the resulting stack result. If execution aborts, fail.
• If result is empty, or its top element has numerical value 0, fail.
• [from BIP141] If scriptPubKey is exactly equal to an OP_n (with n between 0 and 16, inclusive) followed by a direct push of exactly 2 to 40 bytes inclusive:
  • If scriptSig not empty, fail.
  • Run segwit validation with the 2-to-40 byte push in scriptPubKey as program, the n value as version, and witness as input (see further). If this execution aborts, fail.
• [From BIP16] If scriptPubKey is exactly equal to OP_HASH160 + a 20 byte push + OP_EQUAL, run P2SH validation:
  • If scriptSig does not consists of only pushes, fail.
  • If result is empty, fail.
  • Interpret the top element of result as a script, and execute it, with the rest of result as input. Call the resulting stack p2sh_result. If this execution aborts, fail.
  • If p2sh_result is empty, or its top element has numerical value 0, fail.
  • [From BIP141] If the top element of result is exactly OP_n (with n between 0 and 16 inclusive) followed by a direct push of 2 through 40 bytes inclusive:
    • If scriptSig is not exactly a direct push of the top element of result, fail.
    • Run segwit validation with the 2-to-40 byte push in the top element of result as program, the n value as version, and witness as input (see further). If this execution aborts, fail.
• If no failure occurred before this point, the input is valid.

• Execute the scriptSig, and call the resulting stack stack. If execution aborts, fail.
• Execute the scriptPubKey with stack as input, and call the resulting stack result. If execution aborts, fail.
• If result is empty, or its top element has numerical value 0, fail.
• [from BIP141] If scriptPubKey is exactly equal to an OP_n (with n between 0 and 16, inclusive) followed by a direct push of exactly 2 to 40 bytes inclusive:
  • If scriptSig not empty, fail.
  • Run segwit validation with the 2-to-40 byte push in scriptPubKey as program, the n value as version, and witness as input (see further). If this execution aborts, fail.
• [From BIP16] If scriptPubKey is exactly equal to OP_HASH160 + a 20 byte push + OP_EQUAL, run P2SH validation:
  • If scriptSig does not consists of only pushes, fail.
  • If result is empty, fail.
  • Interpret the top element of result as a script, and execute it, with the rest of result as input. Call the resulting stack p2sh_result. If this execution aborts, fail.
  • If p2sh_result is empty, or its top element has numerical value 0, fail.
  • [From BIP141] If the top element of result is exactly OP_n (with n between 0 and 16 inclusive) followed by a direct push of 2 through 40 bytes inclusive:
    • If scriptSig is not exactly a direct push of the top element of result, fail.
    • Run segwit validation with the 2-to-40 byte push in the top element of result as program, the n value as version, and witness as input (see further). If this execution aborts, fail.
• If segwit validation did not trigger, but a witness is provided in the transaction input, fail.
• If no failure occurred before this point, the input is valid.

As of January 2021, "high-level" script validation with all active consensus rules on the network is approximately this:

• Execute the scriptSig, and call the resulting stack stack. If execution aborts, fail.
• Execute the scriptPubKey with stack as input, and call the resulting stack result. If execution aborts, fail.
• If result is empty, or its top element has numerical value 0, fail.
• If scriptPubKey is exactly equal to an OP_n (with n between 0 and 16, inclusive) followed by a direct push of exactly 2 to 40 bytes inclusive:
  • If scriptSig not empty, fail.
  • Run segwit validation with the 2-to-40 byte push in scriptPubKey as program, the n value as version, and witness as input (see further). If this execution aborts, fail.
• If scriptPubKey is exactly equal to OP_HASH160 + a 20 byte push + OP_EQUAL, run P2SH validation:
  • If scriptSig does not consists of only pushes, fail.
  • If result is empty, fail.
  • Interpret the top element of result as a script, and execute it, with the rest of result as input. Call the resulting stack p2sh_result. If this execution aborts, fail.
  • If p2sh_result is empty, or its top element has numerical value 0, fail.
  • If the top element of result is exactly OP_n (with n between 0 and 16 inclusive) followed by a direct push of 2 through 40 bytes inclusive:
    • If scriptSig is not exactly a direct push of the top element of result, fail.
    • Run segwit validation with the 2-to-40 byte push in the top element of result as program, the n value as version, and witness as input (see further). If this execution aborts, fail.
• If no failure occurred before this point, the input is valid.

• If the version is 0:
  • If the program is not 20 or 32 bytes, fail.
  • If the program is 20 bytes hash:
    • Execute the script OP_DUP OP_HASH160 hash OP_EQUALVERIFY OP_CHECKSIG, with initial stack input. If execution aborts, fail.
    • If the resulting stack is not exactly one element, or that element has numerical value 0, fail.
  • If the program is 32 bytes hash:
    • If input is empty, or its top element's SHA256 hash does not equal hash, fail.
    • Execute the top element of input as script, with the other elements as input. If execution aborts, fail.
    • If the resulting stack is not exactly one element, or that element has numerical value 0, fail.
• If no failure occurred up to this point, return success.

This answer does not include the changes introduced by BIP341 and BIP342, as these are not active on the network. It also does not include various standardness/policy rules.

Source: https://github.com/bitcoin/bitcoin/blob/v0.20.1/src/script/interpreter.cpp, functions VerifyScript, VerifyWitnessProgram, ExecuteWitnessScript.

As of September 2023, "high-level" script validation with all active consensus rules on the network is approximately this:

• Execute the scriptSig, and call the resulting stack stack. If execution aborts, fail.
• Execute the scriptPubKey with stack as input, and call the resulting stack result. If execution aborts, fail.
• If result is empty, or its top element has numerical value 0, fail.
• [from BIP141] If scriptPubKey is exactly equal to an OP_n (with n between 0 and 16, inclusive) followed by a direct push of exactly 2 to 40 bytes inclusive:
  • If scriptSig not empty, fail.
  • Run segwit validation with the 2-to-40 byte push in scriptPubKey as program, the n value as version, and witness as input (see further). If this execution aborts, fail.
• [From BIP16] If scriptPubKey is exactly equal to OP_HASH160 + a 20 byte push + OP_EQUAL, run P2SH validation:
  • If scriptSig does not consists of only pushes, fail.
  • If result is empty, fail.
  • Interpret the top element of result as a script, and execute it, with the rest of result as input. Call the resulting stack p2sh_result. If this execution aborts, fail.
  • If p2sh_result is empty, or its top element has numerical value 0, fail.
  • [From BIP141] If the top element of result is exactly OP_n (with n between 0 and 16 inclusive) followed by a direct push of 2 through 40 bytes inclusive:
    • If scriptSig is not exactly a direct push of the top element of result, fail.
    • Run segwit validation with the 2-to-40 byte push in the top element of result as program, the n value as version, and witness as input (see further). If this execution aborts, fail.
• If no failure occurred before this point, the input is valid.

• [From BIP141] If the version is 0:
  • If the program is not 20 or 32 bytes, fail.
  • If the program is 20 bytes hash:
    • Execute the script OP_DUP OP_HASH160 hash OP_EQUALVERIFY OP_CHECKSIG, with initial stack input. If execution aborts, fail.
    • If the resulting stack is not exactly one element, or that element has numerical value 0, fail.
  • If the program is 32 bytes hash:
    • If input is empty, or its top element's SHA256 hash does not equal hash, fail.
    • Execute the top element of input as script, with the other elements as input. If execution aborts, fail.
    • If the resulting stack is not exactly one element, or that element has numerical value 0, fail.
• [From BIP341] If the version is 1, the program length is 32, and this is not operating inside a P2SH wrapping:
  • If the input consists of 0 elements, fail.
  • If the last element of input starts with byte 0x50, call it the annex and remove it from the input.
  • If the (remainder of) input consists of a single element, evaluate it as a Taproot key path spend:
    • The element is interpreted as a single BIP340 (Schnorr) signature for the transaction, using a message hashing scheme described in BIP341. If the signature is invalid, fail.
  • If the (remainder of) input consists of two or more elements, evaluate it as a Taproot script path spend:
    • The last element of input is interpreted as a Taproot control block, encoding a leaf_version, an internal x-only public key, and a Merkle path, and the penultimate element of input is called the taproot_script. The control block and taproot_script are removed from input.
      • Recompute the Merkle root of the script tree, starting from the leaf (leaf_version and taproot_script), and then tweak the internal x-only key with that Merkle root. If the result does not match the 32-byte witness program, fail.
      • [From BIP342] If the leaf_version is 0xc0, taproot_script is evaluated according to the Tapscript validation rules, with the remaining of input as initial stack. See BIP342 for how this differs from normal script execution.
• If no failure occurred up to this point, return success.

Source: https://github.com/bitcoin/bitcoin/blob/v25.0/src/script/interpreter.cpp, functions VerifyScript, VerifyWitnessProgram, ExecuteWitnessScript.