Answer: There are all sorts of materials you can use. You can use painted or stained wood, rot-resistant wood like cedar, or even things like metal and plastic. Here are a few considerations:
The boxes generally look best if they are the approximate width of the window. They should be at least 8 inches wide, and 8 inches deep for good plant growth.
You can use 1" thick boards held together with waterproof glue and screws, or more complex joinery. Whatever you do, be sure to drill several drainage holes in the bottom. Plastic liners will help by keeping moisture in, and protecting the wood from excess water. Be sure to purchase the liners first, so you can be sure you build the box to fit. Use strong brackets placed no more than 18" apart to suppor the box and attach it to the house. A box filled with moist soil is surprisingly heavy! (On that note, be sure to mount the box before you fill it with soil and plant it--otherwise, it will be very heavy to lift.)
The book "The Backyard Builder" by John Warde, editor (Rodale Press, 1985) contains complete plans for building window boxes, as well as hundreds of other woodworking projects. Good luck!
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