Creating an valid address based on an invalid public key
Bitcoin addresses are the pubkeyhash (not pubkey) plus version and checksum information, encoded in base 58.
Bitcoin address = version + RIPEMD-160(SHA-256( Public Key )) + checksum
The steps for converting a public key to an address can be found here:
Since the address uses the pubkeyhash not the actual pubkey we can exploit this by hashing an invalid pubkey (one which can't possibly exist) and thus produce a valid address from an invalid pubkey.
So to start we find an invalid public key. All valid public keys begin with 0x04. We can exploit this fact to create a invalid public key, that is one in which we can provably say there is no corresponding private key. Since spending coins requires signing the transaction with the correct private key, an address which has no known private key is unspendable. By using a public key which is known to not have a private key others can confirm that no private key exists.
A valid Bitcoin Public key (not address):
An invalid public key
There is no private key which will produce a public key of 0. We can then generate a valid Bitcoin address from this invalid public key. The Bitcoin network only verifies that an address is in the right form, length, and has the right checksum when "validating it". Most of the time the public key is unknown so no check against the validity of the public key is performed.
Publish both the address and invalid public key to allow verification that the public key corresponds to the bitcoin address and that the public key is invalid. Any coins sent there can never be spent and third parties can verify this for themselves.
Technically it is possible but improbable for more than one public key to have the same Bitcoin address. This is called a hash collision. If public key p1 and public key p2 both hash to the same address A then privates keys for either of these public keys can spend the funds. However the likely of this happening is very low. Unless RIPEMD hash algorithm is broken the probability of finding two public keys which generate the same hash (Bitcoin address) is 1 in 2^160 which is far beyond our computational power to locate.
Nothing Up My Sleeve Number:
Using a "nothing up my sleeve number" (such as a single zero, all zeroes, single repeating digit, sequential numbers, digits of pi, etc) is not required as any invalid public key is equally unspendable but it would improve public confidence that you haven't already found a collision (as improbable as that is).
If you just take a random invalid key like say:
Some may question why you chose this specific key. The fear would be that you choose this key not randomly but because you have stumbled upon a collision between this key and a valid key. There is no way to prove the key is random thus the fear will always remain. Cryptographic functions (like RIPEMD or SHA-256) often used "nothing up my sleeve values" to dispel the fear that random seed is not random but chosen to enable some cryptographic flaw or "backdoor" in the algorithm.