How do you transfer a domain name?

I am with aplus.net… I registered my domain with them several years ago. They now blow the biggest donkeyhonkers I’ve ever seen. They went from being smooth and user friendly to absolutely impossible to navigate. I hate them, and I don’t want to use it anymore. I want to transfer my domain.

I barely know the first thing about websites (I can write HTML, that’s about it), so transferring all my crap sort of terrifies me.

How does this work? Am I going to have to manually upload all my bazillions of pictures, graphics, media, etc.? Am I going to have to save all of my .html files’ code so I can just copy/paste it at the new place?

I’m at work so I can’t really do a whole lot of looking into it at the moment, and I’m pretty sure that even if I did, I’d still be stuck with the same questions, since from what I can tell, these hosts expect you to know everything already.