For the box I purchased a Large Plastic Storage Bin from Target for $13. It's about 24x14x16. I wanted something really wide for doing several skeins of yarn all lined up, and tall for large bobbins. You may not need as large of a bin if you are shooting something smaller (like jewelry or beads). The clear bin works as a great light diffuser and you can store all the lights & backdrops in it when not in use.
For light I purchased 3 clip-on office lamps from Target for $6 each. I have another office lamp in front of the light box that I already had. That is optional. If you are using a smaller box you might not need a light in front. My box is big so I supplemented a lamp in front for a cleaner look.
The light bulbs in the lamps are 60 Watt and cost $2 for 4 bulbs.
The white background is a roll of craft foam I purchased at Michaels with a 50% off coupon. It is normally $8 but I got it for $4. The roll is 36x60 inches. I cut the 36" to 24" to fit into the plastic bin, and taped it to the interior top of the box with packing tape. Just in case it gets dirty, I'll be able to roll it and use different sections back & front. I like that it is a matte finish (no glare or shine in my photos) and it won't bend permanently like paper. It also stores easily. If you're using a smaller box you can also use white posterboard for your backdrop. Or a smaller piece of craft foam. I've seen some fiber artists use cute scrapbook paper as the backdrop in their lightboxes with charming results.
And that's about it.
Plastic Bin = $13 (you can save $ by buying a smaller one)
Foam Backdrop = $4 (use a 50% off coupon)
3 Lamps = $18 (check out a thrift store too!)
Lightbulbs = $2
TOTAL COST = $37
Below is an unedited photos taking in the lightbox with my little Canon PowerShot SX110IS using the "Tungsten" white balance settings (for indoor photos).