1.
Tools-Jigsaw, router, tablesaw, you need something to cut a circle out of a piece of wood and something to cut the wood. You are also going to need your choice of screws or nails, I recommend screws. You need a drill, drill bit to predrill the holes so the wood will not split, countersink bit, liquid nails or some type of wood glue, silicone sealant if your cuts are not perfect, 3/4" MDF, and carpet and spray on carpet glue if you want your box to look nice.
2.
Home Depot, Lowes, or any type of hardware store that sells MDF.
3.
Depends on what you already have. A sheet of 3/4" MDF is roughly $20 (you will most likely only need one sheet). You can estimate the cost of everything else.