I used my garage. It was February in Minnesota, but I was lucky to catch a warm weather spell during my project.
Jigsaw
A blade with more teeth per inch is desireable. Fine cuts are needed for the racetrack.
Ruler/Straightedge (or marking rounded cuts)
I didn't have one of those large rulers with a hole in one end, so I used a piece of wood paneling and drilled a hole in one end and marked my measurements on the wood with a Sharpie... it worked fine.
Drill
I actually used two drills, one cordless and one non-cordless. The non-cordless came in handy for some of the heavier drilling. One drill should so you just fine.
Kitchen Knife
Ideally an electric bread knife will be the easiest way to cut the foam, but a standard serrated bread knife worked fine.
Electric Staple Gun
I didn't have one, so I picked one up from the Home Depot. I used a manual trigger staple gun on a previous table and I can tell you the electric gun is worth the extra $20-$30. It will help prevent carpal-tunnel syndrome.
Hammer
Helpful for pounding in some of those pesky staples that won't go all the way in.
Blowdryer
This is optional, but I found it helpful for heating the vinyl and stretching it over the rail. It helped prevent wrinkling.
Plyers
Helpful for removing some of those pesky staples that won't go all the way in.
Box Cutter / Razor Blade / Scissors
For trimming vinyl and fabric.
Drill Bits and Spade Bit
Drill bits for pre-drilling guide holes and well as a spade-bit for counter-sinking the T-Nuts.
Paint Brush
For application of the clear gloss polyurethane.
Hole Saw (optional)
A hole saw would make cutting the drink holder holes easier. I used a jigsaw, but if a I built a racetrack again, I'd buy a hole saw that attaches to your drill.
Hacksaw
I cut down the metal table legs 1.5 inches. This brought the height of the table down to 29 inches.
Saw Horses
Or construct some other way of elevating your materials.
C Clamps
Used in different applications throught the project.