I Need Help With Telephoto Lenses?

Ok I am looking for a decent cheap telephoto lens around $200 preferably cheaper. I am a little more experienced than an amateur, and don't know everything about lenses (this is my first Dslr). Anyways, here's my question(s), what does it mean when the zoom factor says like 4x or something. Is it the same as like on a point and shoot camera when it says like 20x zoom or what. I say that because my old powershot sx 20 is was 20x zoom. 4x zoom sounds a little weak for $150+, second what would be your recommendations for a good relatively cheap telephoto lens ?