Hi,
As Galfonz said, a driver chip is a hard requirement. Okay, you could also do this manually with FETs, but you'll need FET drivers, as you FPGA pins go to 3.3V maximum, and they cannot drive large peak currents currents as the one you need to quicky switch a FET.
I also used PWM to drive a motor before, but more as a hobby project. There are in fact actual PWM H-bridge ICs, see e.g. this one:
http://www.ti.com/product/l293 (
http://www.ti.com/product/l293), which I would recommend for your application.
I would also add a capacitor in parallel to the motor, to provide a path to the motor's coil current when the PWM is in idle phase, as seen e.g. here:
http://www.ermicro.com/blog/?p=706 (
http://www.ermicro.com/blog/?p=706). I'm not an expert either, so if you want to make a real product out of this, you should read some more about that topic. For a hobbyist project, however, just using a controller chip with the datasheet's recommended circuit should be enough.
Best regards,
GooGooCluster