A good starting point is to educate yourself about the diffrence between Raster and Vector Graphics. And then...
The best tutorials I would recommend would be from Lynda.com :
Look for the Illustrator CSX(depending on what version you have) Essential Training and then proceed to mare advanced titles.
You can also try Total Training.com , the are simmilar to Lynda.com, you can start with the basics and then go to guru stuff...
Or another nice one is Real world Illustrator[thx to AG for this one]:
For some diffrent stuff you can try some none-video tutorials from websites like:
And just google for illustrator tutorial and you'll find tons of stuff, maybe even in your native language.
(if your not enlish, I was lucky and I did found some tutorials in Romanian :D so if you know romanian these are very cool: