Try using a cup with a straw. They make spill proof cups with straws which I learned are better for speech development (as they use different muscles to suck from a straw as opposed to the sippy kinds). In order to get my son to drink from one of those instead of a bottle, we gave him apple juice out of one of the Mott's AJ juice boxes. We squirted a little in his mouth and in less than a day he learned how to suck up the straw. Then we put some (immediately) in a straw cup and he got the hang of it quickly. After that, we put whole milk in it and offer it to him during meals, and whenever we think he's thirsty (after playing outside). As your child gets older, he will ask for something to drink throughout the day. Our pediatrician only recommended 24 oz of milk and our son has no problem getting that daily.
Also - there are different kinds of straw cups out there... try to stick with the ones that look just like a straw (Dora/Diego character ones, etc.). The other brand that is a transparent color (green, orange, etc.) is a little trickier for the kids to learn as you need to squeeze and suck at the same time... I think it's a little different than the way they get it from a bottle.
Good luck!!
P.S. We skipped the whole sippy cup stage and went straight to straw cups. It's been awesome for restaurants since most of them give kid's cups with straws. We never need to worry about bringing his cup with us! Just a thought...