Using hydrogen bombs you can get something like Project Orion to about 10% the speed of light, but not much faster. Project Daedalus is a more advanced design with the goal of accelerating an unmanned probe to 12% the speed of light [1]. The only somewhat practical ideas that seem to go beyond that involve antimatter fuel: not quite as easy to handle and well understood as nuclear bombs but certainly more attainable than giant black holes. There are a few designs that should allow travel at 60-80% the speed of light