Basically, you will end up with three sides of an elongated box. If you can afford 3/4" plywood, then it will support itself and you won't need any framing, except ledger blocking on the ceiling.
First, the vertical sides need to be attached to the ceiling. If it will be going across the floor joists, then just nail a small (1x2) ledger, or blocking to the joists and then nail your sides to them. If it will be going parallel to the joists then you need to put some pieces of blocking every 2 feet between the joists (usually measuring 14 1/2" long), then nail your ledger, then your sides. Then, when you have both sides on, just nail the bottom to the sides. If the bottom piece is less than 3/4" thick then you need some blocking between the sides so the bottom doesn't sag. You will then need some corner moulding or something to cover the end grain. The only way around this moulding is to rip the edges at 45* for a long mitered corner, which usually doesn't work that well and is a lot of work. If you use screws to attach everything, and small brads to nail your moulding, then later on you will easily be able to take it apart if you ever need to work on the ducts etc.