Hi Heather,
We just finished potty training our Matthew, who turned three in June as well, coincidentally.
I think at this age, you just have to bite the bullet and do it. The diapers that we use do not help them learn what feeling wet is, etc. He'd been going at his daycare pretty well, and wasn't doing it at home, so I decided that was our fault, for not making him.
I told him that the doctor said no more diapers one weekend, took the day off work, then had him go on the pot every hour. Every time that he went successfully, he got to put a stamp on a cheap white tshirt that I bought on clearance at Target, and wrote "I DID IT!" on the top. For each day we were working on it, he had a prize that he helped pick out. Day one, if after the conversation with the doctor and the doctor said he did well that day, he got a clown cone. The next day, dinner at McDonald's. (If they help pick the prizes, they are more likely to be into it.) The third day was a toy I picked up at Target on clearance, I made it a sizeable box, to pique his interest. He had a few accidents, but after two days, didn't even really need the incentives. (The first two days, there was a great deal of whining, as well, but I held firm.) On Monday, he got to wear his tshirt to school and tell all his friends and teachers about his accomplishment.
This worked. You have to patient, and not yell, and praise when they go, and tell that they did not do their job when they have an accident. Putting all the blame on the "doctor" also takes away an incentive to argue and negotiate with you -- no, I'm sorry, that is the rule, you can't get the clown cone unless you go and the doctor thinks you did a good job today. And it helps you not be tempted to give in to them.
At this age, from various blogs and things that I've read, the cold turkey approach has been succesful. If they think they can go back to diapers, that holds them up, I think.
This method may not necessarily work for a very young child. At fifteen months, as one woman hear posted, I sincerely doubt that the child is physically capable yet of being truly potty trained. If they are interested, though, I would be putting them on. My seventeen month has been interested in all this, he is interested in everything his big brother does, so I'll stick him on the pot if he wants, but I know that he isn't really ready. My eighteen month old neighbor, however, is indicating when he needs to go poo already, and even pee sometimes. They are all different, and even though the eighteen month old is probably well on his way to being trained at a much younger age then my Matthew, it will take more than a weekend with him, simply because of the age difference.
Matthew is going strong -- they use a sticker chart at school, which he also loves - every time he goes, he puts a sticker next to his name.
Consistentcy is the best with kids. If you are waffling and they know they can go back to using the diaper, that will sink you every time. Good luck!