If you want a complete solution, look at a VNH2SP30-E - Automotive Fully Integrated H-Bridge Motor Driver, made by ST Microelectronics.
Somewhat difficult to use for a hobbyist, as they are surface mount devices and require a good part of the PCB to serve as a heat sink area. However, they're rated for 3x the voltage and 10x+ the current that you require. Studying up on the basic theory of operation should give you better ideas on how to build an H-bridge.
Somewhat difficult to use for a hobbyist, as they are surface mount devices and require a good part of the PCB to serve as a heat sink area. However, they're rated for 3x the voltage and 10x+ the current that you require. Studying up on the basic theory of operation should give you better ideas on how to build an H-bridge.