Yard sales and thrift stores can be very hit-and-miss. When you find them you can get great bargains, but most of the time it’s not fruitful unless you have other reasons to shop there.
When I built my Pokemon sculptures, I was able to do that using a bulk brick tub that lego was selling at the time (set #3033). I bought about 20 of those at $20 each and still ran out of certain parts – that’s why Squirtle’s tail was so small. Sadly, that tub was discontinued a few years ago and the bulk tubs that are available more recently haven’t had nearly as good of an assortment or as good of a price per brick.
Probably the easiest way to get cheap parts is to shop on BrickLink. It’s an online shopping mall just for LEGO. Sellers buy sets in bulk (generally when they have clearance sales at retail stores) and sort the parts, putting the individual pieces on their stores. Then you can go in and order any part in quantity. It’s an awkward site to use, but I think the best way is to start at the Catalog tab, find the part you want in the color you want, and then find a store that has them in sufficient quantity. (Disclaimer: I have my own BrickLink store.)
There’s also bulk brick available from LEGO; usually they’re a lot more expensive that way but once in a while you can find some real bargains. Look for the “Pick-A-Brick” in the LEGO Shop-At-Home Store and if you have a LEGO store in your nearby mall, they have an in-person pick-a-brick wall where you can fill up a plastic cup with LEGO parts for a set price.
And of course don’t forget about buying sets on sale. Look at your local Target, Toys ‘R’ Us, or Wal-Mart for clearance sales, and check Web sites online such as Amazon.com and others. Check for sales at LEGO Shop-At-Home (and try their phone number too, as they have weekly phone-only sales as well).
If you know any other good ways to find bulk LEGO at economical prices, please post it here as a comment….