My recommendations:
1. Watch the Dota thread in community. It's really great. In the OP you'll find lots of info of heroes for beginners and stuff like that. (I always recommend Lich, Wind, Shadow Shaman, Witch Doctor, etc).
2. If you start with supports, you'll get the feel of the game very quickly, even more if you start with carries and start obsessing about last hitting. Give yourself a lot of time learning wards positions (there're a lot... always change them), dewarding, rune timing, harassing (VERY important), item use (also very important, most supports have loads of items crucial to the teamfight (pipe, meka, euls, forcestaff, etc)).
3. Try to pick different heroes. This is a hard thing to do, due to the fact that you'll like your comfort zone. But choosing different heroes, with the same "rol" will help you get the animation attacks, timing, and will learn more skills quickly.
4. Use the in game guides. They're really good, especially the ones that have good rating. The best ones almost offers variations due to the game status, like if you need more survivability or less farm and more hit, etc.
And that's that... the game is a BAZILLION times better if you play it with friends. So join fellow gaffers that are in your same situation (starting) by joining in the GAF Steam Group!
Anywho, have fun. The game is GREAT. The lows are really lows... but the highs are so good man... you'll enjoy it a lot. Actually... this reminds me of a drug... :S