To be honest, one of the best ways is to take apart a simple mod and start from there. Set yourself a simple goal, such as "I want to be notified every time I get crit with a big annoying message" and work towards that.
http://www.wowace.com should have a fairly good "Hello World" tutorial that builds up slowly. It's a great place to get started.
A fancy LUA editor isn't really required - I just use Notepad2 with a LUA syntax installed and it works just fine for me. But yeah - start really simple and build your way up.
http://wowwiki.com is your friend as far as API functions go. Experimentation will get you far as well, as the majority of them aren't labeled too well.
IRC is a great resource too and I've found the people in the Ace channel helpful and fun to be around.
