Just to clarify the above, it's 417 Florida Greenway from the airport not 429.
If you take the south exit at the airport you then take 417 to Kissimmee. There will be two manned toll booths which cost around $1.50 each. There's also an unmanned exit toll of 50 cents. Make sure you have the 50 cents for this.
We take exit 2 for Celebration then take a left when you get out to 192 also called Irlo Bronson Memorial Hwy. Take a left onto Formosa Gardens Blvd (intersection by Red Lobster, about 5-6 km), then take a right onto Funie Steed Rd after about a km. The entrance to Emerald Island has a dolphin fountain.
We usually take this way because the traffic is a lot less than the north exit and 528 and I-4. 528 has a toll or two also so it doesn't make much difference moneywise.