We could have never afforded to build these had we not found used cedar 2x6's that the parks service was throwing out and redwood 2x6's salvaged from a deconstructed deck. Those two windfalls yielded enough good rot-resistant wood to work with.
Additionally, I added a soaker-hose irrigation system built into the planters with quick-connect fittings for easy watering.
You will need cedar, redwood, or similar rot-resistant wood. Some people use pressure treated wood, since the new types don't contain arsenic, but some people are still wary. Cedar lasts longer anyhow, and I think it looks good. New, it's really expensive, but look for old decks, playsets, pergolas, etc. that you can haul for free.
Use a good coated, rust resistant screw to assemble. I used 3" coated deck screws. Each layer is assembled with 3" galvanized nails.
6 -- 2"x6"x7'
6 -- 2"x6"x3'
2 -- 2"x6"x7' 10" mitered 45 degrees toward center on each side
2 -- 2"x6"x3' 10 1/2" mitered 45 degrees toward center on each side
8 -- 2"x6"x 16 1/2" for corners
Circular saw or crosscut hand saw
Strong drill or screw gun, preferably corded