Anything & everything. Never know what you're gonna encounter.
When I first started, I knew how to do pretty much everything to a bmx bike, except stuff like adjusting unsealed threaded headsets, unsealed hubs, etc, were a pain in the ass at first but are now a breeze.
As for mountain/road bike stuff.. I knew next to nothing aside from the basics. Derailleurs still give me a hard time (usually just piece of shit ones off Wal-Mart bikes) but almost everything else is pretty easy, but that doesn't mean I never run into problems every now & then. So basically, if you could take apart a mountain bike(brakes & cables too), and reassemble it, you'd be right on track. Derailleurs though can be a bitch to work with sometimes getting them to work juuuust right. Rear shocks are another thing that can be a bitch, but luckily we don't see many people needing that messed with enough to the point that it IS a bitch. Personally I've never even worked on one.
Other than that, a lot of stuff is just common sense really. Until someone brings in an odd item like a wheelchair bike or something, then you're like dafuq.
I'd say the majority of customer work is mostly piece of shit mountain bikes or bmx bikes being brought in to be tuned up/fix flats, but occasionally we do get a nice mountain bike or bmx bike to work on. Same with wheel builds, mostly junk shit, sometimes nice.
Rest of the work is assembling new bikes, stocking parts, pricing them, figuring out what we're running low on/could use, helping a customer figure out how their bike rack goes on, talking to Jehovah's Witnesses that randomly come in trying not to make fun of them, and occasionally if I run out of stuff to do, I'll either clean my bike, do maintenance to it, clean the shop, or rearrange shit. Pretty much it in a nutshell.
Sometimes the best part is playing bmx dvds when your friends come in on a slow day and just talk and chill.