We transitioned only because he learned at daycare, that was days on end of them showing him how to tip that cup and also modeling by the other kids. We had no luck really at home. We started him with a straw sippy at a young age and he did well with that for water, then upgraded to the cups you have to tip once he learned that skill. He lost interest himself in both the morning and lunchtime milk bottle, we waited until he did. Then we only offered the cup - 'here's your cup of milk' - if it's the only thing on offer after a few days they get the idea. They are really smart at this age.
He still has his bedtime bottle, it is our only Spirited child tamer so we aren't going to get rid of it anytime soon.
I find that if you just keep offering over and over and over eventually they get it. They need lots of practice. And then they tend to show you when they are ready to dump the bottles.