If you are staying at a WDW resort, you will be given a parking pass for your car when you check in; the pass with have your resort name and the dates of your stay printed on it. Put this pass in your windshield where it's plainly visible.
So long as you have a valid WDW resort parking pass in your windshield, you will be waved through the theme park toll plazas without paying the fee.
Additionally, if you are staying at the Swan and Dolphin, you also get to park for free, but they don't give you a parking pass; you have to show your Swan/Dolphin room key at the toll plaza.
And of course, Annual Passholders get to park for free at the parks, as well. Again, you have to show your pass at the toll plaza, so keep it handy.
