Simple ways to add horse power?

Hello again,

As some have already noticed I don't know much about cars. Actually, to say that I don't know anything about cars would already be saying too much. Still however, I am interested in adding a few more pony's to my 2001 S4 and improving performance.

I am curious what some possible ways of adding horse power would be...both expensive and affordable? What have some of you done to your cars to boost the acceleration/speed a bit more? I've been reading things online but in many cases I either don't exacly understand the terminology or the suggestions seem all out strange(like removing the air filter completely....which certanly would boost horsepower as I can imagine but then I would have all sorts of muck in my engine). I've read about the K/N(I think) Air Intake System which is suppose to boost horse power and wondered if anyone has experience with that.

Thanks in advance for all your suggestions.