Sure you can learn on your own. I've basically taught myself and I am no expert sailor. I've certainly made my share of mistakes on the water and mostly damaged my pride (and a little chipped fiberglass at times). I also sailed with other sailors on other people's boats and that help too.
Take any opportunity to sail, dinghy or keelboat. I learned on keelboats but I've sailed dinghies. I read the Annapolis Book of Seamanship cover-to-cover and a few minutes on the water will teach you more than hours on the couch.
A 20 foot boat on a small river is ideal learning experience. Within an hour you should be able to fit all your basic sailing theory together be able to sail the boat, tack and gibe. Everything else is details unrelated to actually sailing such as navigation, docking, undocking, maintenance, etc. Being under sail has always been the easiest part. It's everything else that makes the experience "interesting". For me, docking and undocking is the most stressful aspect of sailing.
Best of luck and have fun!
SV Ruff Heeler
1982 C-27 #5052
Rhode River, MD