Find a local woodturning club.
If you have no idea who or where they are, ask the folks who work at the local library, or the shop class teachers in the local Junior High, High, and Middle schools, Voc-Tech schools, college(s) and / or universities.
Go to a meeting or two, and ask about classes.
Take a class, and use as many different lathes as the class offers opportunity to try. We turners love to share. You might even find a buddy who'll give you private lessons for the fun of teaching you.
When you find a lathe you like, ask where to find a good used one you could beg, borrow, or buy. Keep an eye on estate sales, garage sales, and the like.
Woodcraft carries some reasonbly priced mini lathes. They periodically go on sale.
Check with your local hardwood dealers.
Talk with the guys at lumber yards, and the tool guys at the hardware store, home centers, and so forth.
They just might have buddies who have or had interest in turning, and know who to ask for local leads. Just about two weeks after you get your first lathe, three more will come knocking on your door, asking if they can come in and play. It never fails.