There's been quite a lot of research into this. The most famous examples are Project Orion, which would use fission bombs to work against a "sprung" plate, and Project Daedalus which, if I recall, would use lasers to induce fusion in small pellets.
As I recall, there was even a proposition to launch the former from Earth - and this was also featured in Larry Niven's novel Footfall - whereas Daedalus would be assembled in orbit and launched towards (I think) Barnard's Star.
In terms of power - both spacecraft had a "pusher plate" which would absorb the blast and push it forward, with some sort of suspension to cushion the fragile beings inside. The blasts themselves - well, even a small nuclear explosion is going to put out a fair shockwave, I'd imagine.
I'd guess that Wikipedia would be your friend here - or any passing astrophysicists...