I've been learning without lessons and am about 1 year in to this process now. I had been sailing about 6 times with a friend and decided I needed to do this for myself. I looked at the cost of lessons vs the cost of buying an old boat and decided to go for the boat. I spent 3k for an old but well kept boat with good sails. Ready to go the day I bought it and the PO took me out for a sail that day to get me familiar with it.
Here's my thoughts on this process:
Folks have already advised a lot of reading. If it's related to learning sailing and is available on the web read it. Free is a great price for knowledge. Search the various forums for more critical advice too.
EASE into it. If you can start in an area without crazy winds and currents it's a lot easier. Just cruise around protected waters for a while and then start making small pushes out to more unprotected areas a little at a time.
Don't expect it to be relaxing for a good while. Every time I go out I'm facing a challenge and it feels like it. There's no kicking back and sipping rum drinks at this point. I'm hyper aware of everything and on edge a lot. All I worry about is getting myself and the boat back in one piece. There are moments of bliss but they're the exception. Like screwing up my return timing and coming in near dark. Sunset was amazing but I would never have seen it from the water without the mistake.
It's OK to scare yourself a little. You have to push your comfort zone a bit each time in order to keep learning. Often the best feeling comes when back in the skip and realizing that I handled something new and survived
So yeah... buy a small boat you can manage... sail with a friend a time or two to get familiar and then ease yourself into it one new experience at a time.