Is there a paper with a formal description of a Litecoin? And a paper explaining what a miner does? I would like to understand how to mine "manually", I mean I dont need a tutorial on how to install classic tools, but I would like to understand the process of mining.
You will have to read Satoshi Nakamoto's original paper on Bitcoin.
What you are asking about has nothing exclusively to do with litecoin or any other particular cryptocurrency.
The 30-second version of how Bitcoin and all derivatives work:
Every "endpoint" has an address. This is the public key of an Elliptical Curve Digital Signature Algorithm. The person who has that address keeps the private key in their "wallet" software. When sending coin the source private key and destination public key are used to cryptographically sign the transaction.
To record transactions, there is a block chain. Each block is just a list of transactions plus a bit of verification information. That verification information includes a reference to the previous block (keeping the whole system a linear chain), a cryptographic "signature" confirming that the information in the block hasn't been tampered with, and a Proof of Work. There's some other miscellaneous information as well, but this is the important stuff.
The Proof of Work for BitCoin is SHA256. For Litecoin it's scrypt, which is based on SHA256 but with functions added that demand large amount of RAM. Prime coin uses prime number interactions, similar to RSA public key cryptography. These serve as proof of work by selecting a know output and figuring out what input produces that selected output. The functions are explicitly chosen because they are one-way functions. There's no way to figure out the input which will produce a chosen output without exhaustively trying lots of inputs.
The first so many blocks produce coins; the exact number was set when the currency was created. For Bitcoin it was 50 coins per block, for the first 210,000; after that half as many for the next number of blocks. Eventually less than 1 coin is produced per block, resulting in no more coins being created.
People don't actually send coins to each other. They tell the world that they have transferred the coins to the destination address. A block makes the transaction permanent, and the world agrees the destination has that much more coin. This is fundamentally different from the real world. IRL I give you $5; you then use that "token" to prove to others that you have money. In the virtual currency world, I tell everyone you have +5coin, they all agree. When you want to spend the 5coin they recognize that you received the coin and haven't spent it yet based on my transaction and a lack transactions showing that you spent it.
If you want to know the specifics of how scrypt works, check out the source documents.
In a comment you asked what a BitCoin is. To understand this, you'll have to start with "What is a dollar?". Both are units of denomination, like any fiat or virtual currency. Neither have any intrinsic value; virtual currencies have no physical existence. It will get you the same thing a dollar will - that is, you can trade it with someone willing to accept the currency. Stores assign prices to the items on the shelf for uniformity and expediting the trading process; but it's not a requirement.
I suppose technically you could mine a coin with pencil and paper. Considering the complexity of the hash algorithms in use, you'd probably generate about one has every 10 minutes (or much worse given the difficulty of most popular virtual currencies).
If you wanted and educational example we could use a different Proof of Work function. Say
i (i + x) mod 10 = 0. In this
i is an nonce, picked semi-randomly from the integer number set. Once we've picked
i we try different values of
x until the function works.
So we pick
i, say 2847, then start picking
2847 (2847 + 0) mod 10 == 9 (that doesn't equal zero)
2847 (2847 + 1) mod 10 == 6 (that doesn't work either)
2847 (2847 + 2) mod 10 == 3 (still not a match)
2847 (2847 + 3) mod 10 == 0 (found it!
This "hash function" is extremely simple, but you can figure it out with paper and pencil.
I had to put "hash function" in quotes as
x is always going to be
10 - i mod 10.
Real hash functions don't have a simple equation like that to find