Figure out which area you want to live in first, the Kissimmee/Orlando area is big and there are a lot of choices. There are some nice areas, we live near Celebration, very close to WDW. I like where we are a lot, but some people would probably be happier in a less "touristy" area.
I agree with the pp about a complex, there are a ton to choose from. Once you figure out which area(s) you want, do a search on apartments.com or forrent.com or just google it. You can try Craigslist too, that's actually how I found my apartment (and got a good deal) but make sure that it's legitimate before you send any money! There are a lot of scams out there.
I would pick a few complexes that you are interested and call them directly to get all the info. You can usually go through the application process online or have them mail the application to you. Don't forget to ask about deals! There are so many rentals right now, you may end up with the first month free or even a monthly discount.
ETA: Also wanted to mention that the cost of living is cheaper here than what I am used to. I was pleasantly suprised when I went grocery shopping for the first time. Unfortunately though, the wages here are lower too.