Here's a "before and after" to give you a basic comparison:
Here are the supplies I used. Nothing terribly fancy and not a power tool in sight.
As you can see, there was a LOT of road tar and crud stuck to the inside of the wheel. Since the spokes are fairly open, this was quite noticeable from the front side.
The first step was to use Bug & Tar removal to get the large chunks of crud off the wheel.
Step two was to (gasp!) WET-SAND the wheels with 2000 grade paper and a clay-bar lubricant. This is a very fine finishing paper used in body shops. I went at the wheels long enough to cut through the pits and scratches.
Next was to use paste polishing compound (I skip using rubbing compound) on a hand-held buffer with velcro-replaceable foam pads. The pad-holder really helps make the job easier.
Once the wheel look very even and smooth, I move on to Mothers Aluminum Wheel paste (the small red tin) and a soft cloth for application/buffing. Work the paste into the wheel until the surface starts to turn black and then buff to a shine.
The finished result as a LOT cleaner and shinier (and my shoulder a lot more sore).
Here's a close-up showing the transformation. It took several hours on a cold, rainy day to do this but now the wheels look awesome and ready for the nice weather.
Mark