-A good place to start is at the local night school, adult school, park and rec district, junior college, etc. The price is generally very reasonable, and an instructor is included with a fairly complete wood shop. If there are any such institutions nearby, I'd start there.

-But this is no different from doing anything frugally.

You go to the library, and get some books out about woodworking. Or you go to a used book sale and buy them there. Then you read up on the topic, to get a feel for what there is and what can be done. Maybe splurge on a magazine on the topic, for really up to date information.

Then with your awareness primed, you start looking at the flyers from places that sell the needed items, and get a feel for what's on sale and how frequently. The common things likely are on sale regularly, so it's best to wait. Some other things likely won't go on sale on a regular basis, so you may not want to wait.

You can also try rummage sales, and even garage sales. Just when I was about to buy a drill press vice, I finally found one in the spring at one of the former, for less than half the price I was expecting it to be when on sale.

Don't buy tools until you actually need them, because you may find you don't actually need them, and if you do, they may go on sale before you get around to using them. Of course, if you find suitable tools at garage and rummage sales, you'd buy them as you see them since they won't be available later. But since you've been wathing the flyers, you have an idea of the prices at the stores, both on sale and not, so you can judge whether it's worth buying that chisel now for a dollar "just in case" compared to the five or ten dollars at the store.

And I'm sure you can get the basics on sale in a very short period of time, including one of those "Workmate" type things that fold up but are for providing something to hold the wood while you work on the project.