Polystyrene. I got 4 x 8 sheets (used for insulation) at Home Depot or Lowes. You can get multiple widths, but I prefer 3/4 inch.
Grout. I use sanded Terracotta colored grout.
Sealer. I use and highly recommend Minwax Polycrylic water-based sealer.
Bucket. For mixing grout.
Brushes.
Past these, it really depends on how extravagant you want to get. I went simple with my first to figure out the styrofoam and how everything went. Beyond that you can get pretty crazy...I did
.
For glue I use a low temp hot glue gun. Hot temp will melt the styrofoam, but the low is perfect and holds tight with no drying time.
I have a styrofoam cutter
http://www.floralsupply.com/cat.cgi?s=FLCRFT60143%20Styro%20Cutter&c=dsgnaccs that is very helpful, but not if you are cutting large pieces, because it has the metal piece that prevents you from going more than 6 or 7 inches into the foam. You can rough cut with a knife and smooth it with this which works well.
Again, I went a little crazy, so I got a Versa-tool
http://www.overstock.com/Crafts-Sewing/Walnut-Hollow-25-watt-Woodcraft-Tool-Kit/3485518/product.html (PS I'm very crafty and have used this for tons of stuff since then)
My first...
My adventurous second try...
If you have more questions feel free to ask!