MarkT:
Perhaps the easiest way to build an H-bridge from discrete components is to start with
good MOSFET H-bridge or half-H-bridge driver chips(*), add 4 n-channel MOSFETS
well up to the power and current and voltage ratings, and follow the suggested circuits
in the driver datasheets. If you have a supply of limited current-sourcing ability
that will help prevent expensive mistakes (lead-acid and lithium batteries are not
forgiving).
I'm going to second this, with the following extra bit: Size the FETs 4 or 5 times larger than your current needs (so you want 10A - pick 50A n-channel FETs). That will give you plenty of breathing room, and it won't be that much extra to spend. You likely won't need heatsinks for a FET h-bridge (with the larger FETs and the smaller current needs), but you might want to leave room for them just in case (or if you want to use it with even larger motors later).
That said - you would still likely to be better off purchasing an h-bridge; since you don't want to go down this route, purchase plenty of spare FETs for the inevitable destruction as you test and play with the h-bridge you do build.