A few questions.

I am curious. I haven't yet shot many great sports photos but want to learn.

I know on most cameras there is aperture priority mode and shutter priority mode. What if you want to be able to control both? As in... have a large aperture but a really fast shutter speed (creating shallow DOF while capturing the action). Is there a way, or are you always limited?

Also, what is "fast lens"? I realize that the lower the f/stop number..f/1.8, f/2.8, etc... are going to be "faster", but why? Does this just mean the camera doesn't have to wait as long to be exposed because it is getting more light?

"I know on most cameras there is aperture priority mode and shutter priority mode. What if you want to be able to control both? As in... have a large aperture but a really fast shutter speed (creating shallow DOF while capturing the action). Is there a way, or are you always limited?"

Use Manual to get the shutter speed and f/stop you want. Then use ISO to get the right exposure.

Also, what is "fast lens"? I realize that the lower the f/stop number..f/1.8, f/2.8, etc... are going to be "faster", but why? Does this just mean the camera doesn't have to wait as long to be exposed because it is getting more light?'

The lower the f-stop, the more light -- the more light, the faster your shutter speed can be to get proper exposure.