DX and LX models have the lower of the engine choices and the LX is nicer then the DX.
EX is the nicest of all with a slightly more powerful engine, sunroof, power accesories, etc.. (body colored mouldings, I think)
Si is the performance variant.
I have listed them in order of increased pricing as well. Check out Hondas website for more info on the different models.
And, welcome to AF. Check out the FAQ section, this shuld answer a lot of your questions about Civics and pretty much any other car stuff. Good luck.