Can you? Absolutely, and air traffic control will treat you (almost) like any other airplane. You are supposedly handled on a first-come-first-serve basis (reality is slightly different with different aircraft speeds, etc.). Do the airlines like it if you slow them down? No, but it's part of the system and the way that it works.
Very often, there are multiple runways at bigger airports, and sometimes there are even shorter runways that are dedicated for airplanes that don't need to land on the same one as the "big boys". Even if not, they will work you in.
Now, that being said, very often there is a better option. As you said, there are usually high fees at the big airports, so landing at a smaller satellite airport can often save you money and save you time because you won't have to taxi as far or sit and wait in line to get out. An extra 15 minutes by car can be better than an extra 30 minutes while taxiing.
As far as being prepared, it isn't really much different than smaller airports other than the fact that ATC is much busier. They don't have the time/tolerance to keep repeating instructions to you, and expect you to be "on your game". When they rattle off taxi instructions like "Cessna N1234, taxi to the ramp via Alpha, Tango, Echo, and Xray. Hold short of runway 23." they expect a quick readback and for you to follow instructions exactly because they need to move on to the next guy.
It will also help everyone out if you don't fly your final approach the way that most people are taught for an entire 10 mile final: very close to your actual landing speed. In fact, you are usually landing on a runway that is 4X+ the distance that you need and you can slow down fairly quickly (especially compared to a jet), so if you can fly an extra 20 (or 80) knots as long as possible, it will be greatly appreciated and keep traffic moving. Make sure that you leave yourself enough time to slow down at the end and above all else, be safe.