I believe that they do, is they take two atoms and shoot them at each other at such high velocity that they merge together, or something. This apparently causes an explosion. I know it's more complex than that, but I am pretty sure what I described has something to do with it.

There is no fusion involved in a nuclear weapon. Perhaps you mean fission? Fusion is colliding four hydrogen molecules at very, very high energy to form a Helium molecule - this releases a lot of energy and alpha, beta and gamma radiation. Fission, on the other hand, uses a neutron at very high energy to split a uranium molecule into smaller, unstable molecules. This also releases a great deal of energy, as well as beta and gamma radiation.
According to my earth and space teacher at my school, humans have never been able to, and most likely will never be able to perform nuclear fission. (It was either fusion or fission, but I am almost certain it was fission)