Unless you are very strong do not construct a box larger than 2 x 4 feet because they will need to be lifted from time to time. Wooden boxes should last three or four years. If built of plywood, use an exterior grade to prevent delamination. It is not advisable to make containers from rot-resistant redwood or cedar because the natural oils that prevent rotting also may be toxic to worms. Sealed with polyurethane, epoxy, or other non-toxic waterproofing material, worm boxes should last quite a bit longer.
How big a box or how many boxes do you need? Each cubic foot of worm box can process about one pound of kitchen garbage each week. Naturally, some weeks more garbage will go into the box than others. The worms will adjust to such changes. You can estimate box size by a weekly average amount of garbage over a three month time span. My own home-garden-supplied kitchen feeds two "vegetableatarian" adults. Being year-round gardeners, our kitchen discards a lot of trimmings that would never leave a supermarket and we throw out as "old," salad greens that are still fresher than most people buy in the store. I'd say our 2-1/2 gallon compost bucket is dumped twice a week in winter and three times in summer. From May through September while the garden is "on," a single, 2 foot x 4 foot by 12 inch tall (8 cubic foot) box is not enough for us.
Bedding
Bedding is a high C/N material that holds moisture, provides an aerobic medium worms can exist in, and allows you to bury the garbage in the box. The best beddings are also light and airy, helping to maintain aerobic conditions. Bedding must not be toxic to worms because they'll eventually eat it. Bedding starts out dry and must be first soaked in water and then squeezed out until it is merely very damp. Several ordinary materials make fine bedding. You may use a single material bedding or may come to prefer mixtures.
If you have a power shredder, you can grind corrugated cardboard boxes. Handling ground up cardboard indoors may be a little dusty until you moisten it. Shredded cardboard is sold in bulk as insulation but this material has been treated with a fire retardant that is toxic. Gasoline-powered shredders can also grind up cereal straw or spoiled grass hay (if it is dry and brittle). Alfalfa hay will decompose too rapidly.
Similarly, shredded newsprint makes fine bedding. The ink is not toxic, being made from carbon black and oil. By tearing with the grain, entire newspaper sections can rapidly be ripped into inch-wide shreds by hand. Other shredded paper may be available from banks, offices, or universities that may dispose of documents.
Ground-up leaves make terrific bedding. Here a power shredder is not necessary. An ordinary lawnmower is capable of chopping and bagging large volumes of dry leaves in short order. These may be prepared once a year and stored dry in plastic garbage bags until needed. A few 30-gallon bags will handle your vermicomposting for an entire year. However, dry leaves may be a little slower than other materials to rehydrate.
Peat moss is widely used as bedding by commercial worm growers. It is very acid and contains other substances harmful to worms that are first removed by soaking the moss for a few hours and then hand-squeezing the soggy moss until it is damp. Then a little lime is added to adjust the pH.
