Where should I start? I assume I'll need to be able to copy files and do some basic tasks if it's going to be of any use.
At it very simplest, you use ssh to connect to another machine, and now you have a command line interface to that machine, so you can use any of the usual command line facilities.
Can you do anything with a command line? If not, you'll need to find a beginner command line tutorial[0]. If so, you'll need to tell us more about what you can do, and why you think it isn't enough.
[0] And if you don't know how to find a beginner command line tutorial, looking up things like that is the first thing you need to learn.
Now a year later the command line just feels natural.
You're going to want some of the basics like tar, grep, ls, ps, et cetera but you'll probably pick things up best as you toy around in the environment.
Enjoy!