Spend a little time with the lessons; they help. Skip to the cross-country stuff if you've got the pattern work down, but try it out. That's the best tip I can give you. FS has all that basic stuff covered in the Learning Center.
Or you can just open the map, take a rough guess as to what your heading should be, and go find the airport, setting up your pattern as you did at your "home" airport (Tip: you'll want to click on the airport on the map to get the airport elevation; add about 1000 feet to that for your pattern altitude).
Of course, if you're flying something big and fast, that method won't work too well; in that case, you're going to need to learn more about serious navigation to get from A to B without getting lost or crashing. GPS helps a lot, among other things; FS will tell you how to use all of it. It's worth checking out.
Asheville, huh? I landed there once. I was trying to get to Rome, GA (on a trip from NJ to New Orleans), but the weather got bad along my route. Got some fuel there, and hopped over to Hendersonville to park the plane and camp for the night (didn't know for sure if they had fuel at Hendersonville). Nice little airport, and some really nice people...

About the names: those are called identifiers; just shorthand, really. I think they were first used for the Morse Code signals specific to radio navigation beacons at airports and along flight routes... four letters (they used to be just three; the "K" is pretty new) are easier than the full name of the airport. The older ones are like abbreviations, but they had to shift to less-recognizable ones as the list of airports grew.