I use Wesley's Bleche White to clean the tires while I'm washing the rest of the vehicle. I spray it on the tire and let it sit for a minute or so. Than I use a scrub brush and scrub the tire really well. I rinse the tire off and do a second spray, scrub and rinse. The most important thing to remember about Bleche White though is that it is strong stuff. I have read about it eating away the coatings on wheels, etc. I have never had an issue with it because I make the sure the wheel and tire are soaking wet before I use it. I also make sure to give the entire wheel well and even the outsides of the wheel well area a thorough rinse after using it on the tires.
Once the vehicle is dry, I use Meguiar's Endurance Gel to get a bit of a shine on the tires. I use a sponge applicator and add a small amount of the gel onto it and rub it into the tire really well. This is one of those products where the more you add, the shinier the tire will be. I do one coat because I like a nice black tire with a slight shine, but nothing too crazy. Using only one coat, I usually do not see any "sling" down the sides of the vehicle and depending on the weather, the shine will last at least a couple weeks.
I have tried other tire shine products and I have not had the great results with anything else that I get with the Endurance Gel. I am a diehard Mother's fan too, so you know this stuff has to be good
! Oh... and it is grape scented so it smells really good too