For the most part, you can repair the tent simply by purchasing a roll or two of Kenyon Repair Tape, which is adhesive-backed ripstop nylon. It's available in several colors—red, black, blue, and green, among others—and one roll ought to be enough for you. Only $3 at REI or Campmor. Simply clean off the area around the burn or tear, cut a piece of tape to size, and stick it on.
On the tent's fly and floor, cover any holes with another Kenyon product called Recoat 3 ($8), which is a water-based sealant that replaces polyurethane coating. That'll help ensure there's no loss of waterproofness. For the mesh, you'd probably be best off sewing the hole shut using nylon thread purchased at any variety or sewing store.
You also can purchase a complete tent-repair kit from Outdoor Research for $13 (available at REI). It has patches of both ripstop and waterproof taffeta, plus nylon thread and other goodies such as a tent-pole splint. Handy to have!
You're probably lucky your car didn't catch fire...
More advice on keeping your backcountry domicile alive in Outside's 2004 Buyer's Guide .