Personally, I use up so few tires that I let my community recycling pick-up handle that.  I have seen tires cut by hand with a knife to make sandals and shoe soles.  I have also seen individuals make them into planters.  At the local marinas they hang them alongside the docks as cushions for the boats.  I have also seen people bury them halfway to line their driveways (if you put a head at one end, it will look like Nessie).

If you want to know how tires are ground up and made into asphalt, I'm sorry, I can't help you.  But I am sure someone on Yedda can.