Oh! My bad =) I should have looked it up first. I always thought it was take the unstable uranium isotope and surround it with a horrible amount of explosive material which was set at a controlled time to pressure the uranium into a cascading reaction. Turns out, I'm running on the 1940's Popeye cartoon explanation =[
You're right but for the name. That's how the fission nuclear bomb works. Then you combine it with a heavy hydrogen fusion stage to get a thermonuclear ('hydrogen') bomb.
No, the person you're replying to is right, the bulk of the energy is from fission. What the fusion does is serve essentially as a "tamper" - it's in a ring around the fissile core and as it explodes it compresses the fissile core. Since the fission rate increases exponentially this tamping dramatically increases the overall energy yield.
No, that is NOT what the 'tamper' is or does. See my (or various other) nearby comments where I describe the actual process, or just read the Wiki article linked in another comment...
https://en.m.wikipedia.org/wiki/Thermonuclear_weapon
Edit: just acknowledging the funny set of identical replies!