Vanilla textbook RSA does not include "padding and stuff", the term "textbook RSA" generally refers to simply encoding a plaintext message as an integer and raising it to an exponent. Implementing this is pretty easy, just follow the steps outlined on Wikipedia. You can easily translate those steps into some given programming language.
Based on the rest of your statement, it sounds like you want to implement a real-world encryption/signing scheme using RSA, but not some higher protocol that uses it. If so, I would suggest looking at PKCS #1 v2. It's an authoritative specification for several such RSA padding schemes. (RSA-OAEP is probably the most recommended padding scheme for encryption if that's what you want.)