Football Lingo

As a naturalized citizen who's lived here for most of his life, Football used to be foreign to me. I grew up knowing soccer and baseball but for the first years Football was a mystery.

Now I have a pretty good grasp of football and enjoy watching games on TV. But then I come across something like this, and I am stumped and can't decode it. If only there was a good football tutorial (don't worry I already have "Football for Dummies".)

This is from "Oh, did this unit of the Patriots struggle against the Jets", in the Boston Globe.

"On the first 12 plays of the game, the Jets ran four plays each out of their base 3-4, their nickel package (four linemen, two linebackers), and their dime package (six defensive backs)." (from The Boston Globe

Now I have some questions. Nickel to me means five. So how does that turn into four linemen and two linebackers? And Dime to me means ten. How does that translate into six defensive backs?