An Orion pulse drive would have one God-awful heavy mounted shock / pusher plate on the rear of the craft. Not sure about the materials engineering but it would be strong and a good thermal radiator. The 'bombs' would be shot out the back and possibly ignited with laser fusion or the standard fission type. I think they were talking about 1 per minute up to one ever 10 seconds.
The shock wave from the blast would 'push' on the plate and provide thrust for ship.
Are they possible using today's material science ? Yep. The outer space treaty of 1967 prohibits nuclear detonations in space though. Biggest block to space development for the US ever made.
Any other questions ?
The postive benefit is that you could launch something the size of an aircraft carrier in a single stage launch from the floor.
The bad news: your launch site gets a little 'hot'
Any other questions ? Whole bunch of 'em, but I'll cut it down a tad... Are we talking a nuclear detonation the size of a bomb that we are familiar with, or are we talking very small detonations?