The two original Nuclear bombs, the "fat man" and "little boy" operated on the basic principle of sending a radioactive projectile to a larger target mass. They were an implosion type and gun type respectively.

The nodes above have discussed the implosion type rather throroughly, but nonetheless it operates on the principle that you propel a plutonium sphere into a beryllium-polonium core. This requires, however, a non-nuclear explosive.

The gun type bomb operates on the principle that one can send a uranium wedge into a larger uranium target thereby reaching critical mass. The uranium wedge would be projected by means of a conventional explosive ignited by a radio signal.

Again the principle behind each is relatively simple, create enough mass and density that the probability of neutrons from one nucleus impacting with another is high enough for a sustained chain reaction. In principle these are relatively simple, but they are also relatively low yield, with only a few kilotons. Apparently there are all sorts of ways to boost yield.

Its amazing what you can find from the internet and world book encyclopedia