I never had real riding lessons either. The only horses I rode before I got my first one, was rental horses. That was a bit hard, my first year as a horse owner, to go from a horse that followed the one in front of it, to one that I actually controlled myself.
But it all worked out great and I've been trail riding for about 17 years now. I think I've actually gotten pretty good, at least as far as staying on and controlling my horse and such. So yeah, it's definitely quite do-able.
I just sort of got on and rode. And rode and rode and rode. Almost every single day for years and years. Eventually you get good at it.