Yes, I took a basics course at the gym to learn how to belay properly, as well as how to stay safe as a climber.  I think these basic courses are great and everyone should take them before climbing.

Beyond that, before going outdoors I recommend finding an experienced group or mentor, and spend a lot of time with them.  Outdoor classes (anchor building/multi-pitch/etc..) are great, but they don't cover everything.  Having a group to watch over you is invaluable when dealing with such high consequences of failure.  Having someone experienced there to stop you when they see something wrong is more valuable than going out with a pal who took the same course as you...

I think most areas have organizations... if not, check the craig you are planning on cilmbing at and find one associated with it.