You can apply laserable transfer paper to inexpensive wood to make it easier to cut. I recommend TransferRite 582U paper, which can be applied to 1/8" Baltic Birch available from many sources. Use a flat, smooth object (such as a roller, ruler, or even a plastic card like a credit card) to apply from the center to the edges. This works well enough, but watch it carefully; when applying to unfinished wood, the paper may not adhere well enough to hold with detail work.
Did smoke or soot stain your wood or acrylic? Use isopropyl alcohol to dissolve and remove the residue.
Construction and Assembly
Get together your construction toolkit:
Glue: Wood glue or white craft glue for wooden pieces, and acrylic adhesive for acrylic pieces
Toothpicks, for applying glue in hard-to-reach places
Q-Tips, for removing glue in hard-to-reach places
Craft knives or razor blades
Plastic razor blades, useful for scraping off backing material
Wood clamps, for holding pieces while the glue is drying
Wood files for removing splinters and rough edges
Sandpaper
You can adjust designs to use serrated tabs, allowing the pieces to be pressed together with a hammer or mallet. See Dan's post on the Glowforge Owners Forums for more details.