How does password-based encryption technically work?

Say I have some data and a password, and I want to encrypt the data in such a way that it can only be recovered with the right password.

How does this technically work (i.e. how to implement this)? I often hear people use bitshifting for encryption, but how do you base that on a password? How does password-based encryption work?

An example is Mac OS X FileVault

Thanks.

If you give sample code, preferably in C, Objective-C or pseudocode.