Sending people in to space propelled by nuclear weapons might at first seem a totally mad idea, but the physics are actually sound. Much research and development was done during the 1960's, and small scale models using conventional explosives actually flew.
The principle is simple: use the power of a nuclear blast to propel a vehicle forward. The obvious problems are the power of the blast and the safety of the vehicle and its crew. It was envisaged that the ships would use a 'Pusher Plate', through which the bombs would be ejected. This would have an ablative surface and toroidal airbags to cushion the blow, and would have been connected to the rest of the ship by large shock absorbers.
Acceleration experienced by the crew would be smoothed out to acceptable levels. Using nuclear weapons would obviously release a huge amount of energy - far more than conventional rockets - so the ships could be huge, weighing many thousands of tons.
One option which was seriously considered was a mission to Mars.