Erland said:
How does a mixer work? ie. How do you actually record with it.
You don't.

You record with something that records. You can use a mixer while recording, to do several different things, but it is not necessary, and what role the mixer has depends entirely on, well, what you set it up to do.
A mixer takes several signals signal and mixes them. Most mixers also have other neat features such as filters and preamps. Some even have compressors and other effects. Some things that look like mixers also can record. Those are usually called portastudios or digital audio workstations and is a mixer-recorder.
If it is fed into a computer then how do they talk to each other and record?
You need to say 'it' and 'they' a lot less when you ask questions, and start saying 'the mixer', 'the signal' and 'the computer' a lot more.

It gets very confusing, becuase it's not clear what you referr to when you say 'it' if you use 'it' to much.
"Aaarg!! Don't say it!"
"But how can I not say it, if I don't know what it is!"
"You said it again!"
It (ie the mixer) is not fed anywhere. It sits on your table, and will not be eaten.

The signals from the mixer is fed into the computer via a cable. Maybe that answers your question about how "they" talk to each other? Hope so.