We just got back from doing Disney with our daughter, and she is 3.5. She did great and really loved it, but it helped that our expectations were realistic. Here is what worked for us:
1. Rented a house with a swimming pool. Took a break every day to head back for lunch and to swim in the pool (and a nap if possible!), then headed back to the park at night if there was anything to see (parade, fireworks, etc.). Renting a house with a full kitchen really helped on saving money on food by buying and cooking ourselves. Then when DD wanted the $4.00 ice cream cone or $10.00 Mickey balloon, I didn't really care.
2. Used a stroller. Even kids as old as 8 sometimes do better with a stroller - it's a ton of walking around and standing around and their legs can get tired quickly. We lucked out and found a stroller at a thrift store for $10 - then dropped if back off there when we were done (we did Disney parks for a total of 7 days, with 2 days worked in as "off days" so we all got a break, and just stayed "home" to hang around the pool).
3. Got to the park 15 to 30 minutes prior to opening. Was able to get in right when the park opened before lines got too bad. Hit the most popular rides first (Dumbo, Space Mountain, etc.). Was often able to ride multiple times without waiting much in line just because not as many people are there at 9 am vs. 11 am. By 1 or 2 pm, we had had enough, had been on many rides, and were ready to head back for a break (see above).
4. Use Fast Pass wherever and whenever you can. Saved us a ton of time waiting in line later for attractions like the Jungle Boat Cruise and Pirates of the Caribbean.
5. Get the Unofficial Guide to Disney World - tons of great tips, including the ones I mentioned above. Also has strategies for which rides to hit in which order to again, minimize waiting in line.
6. Summer in Florida is HOT. We just got back and had some pretty warm weather - low 80s. By the time we were ready to leave for our afternoon break, we were sapped.
7. My favorites were Magic Kingdom and Animal Kingdom, but all the parks have something wonderful for kids at that age.
8. Remember not to get too upset if your child does not like something as much as you think they should. My DD did well with meeting characters and taking pics for the most part but I know lots of kids don't, while the parents get very pushy about it. On the other hand, she really didn't enjoy many of the shows if they were too loud. She's sensitive about noises, but did a little better the more times we went, as she got used to it. Don't try to get your kids to do anything they really don't want to do, but also recognize that sometimes a little push can be a good thing, in that they realize what they are capable of and then are more confident the next time (scary rides, meeting characters, etc.).
9. If you are staying somewhere with a pool, try not to get too frustrated when they say, after visiting Disney, they say their favorite thing was swimming in the pool. It's their vacation too.
In the end, DD had so much fun, she didn't want to leave. She was distraught as we were packing up to come home - "I not want to leave Disney! I LOVE Disney! I want to stay!"