A discrete h-bridge is fairly difficult to design, primarily to get it to switch fast and to allow for the appropriate dead time.
If you are starting now, I would recommend that you look into h-bridge drivers (high/low-side drivers). They come in many different shapes, depending on your needs.
Generally, you need to decide if you want to have braking / motor hold; if you want to be able to drive high/low sides separately; if you allow enable signaling or not; your desired voltage ratings and if you want under/over voltage protection, etc.
Many firms offer such chips and they are generally easy to use. IRF, Fairchild and On would be good starting points.