Hi! Welcome to the board!
-Buy souvineers off property, they're cheaper.
-At meal times, buy one entree and split if you can. Portions are pretty big and they usually come with a salad or soup.
-For snacking the cheapest item I've found in any of the parks is fruit. You can get apple slices with caramel dipping sauce for about two bucks.
-You don't have to pay for a cup of water. Ask a cast member for a cup of ice water and they'll gladly get some for you.
-If you're going to do a table service meal, try to do it for lunch and then do a counter service for dinner. The lunch menu is cheaper than the dinner menu by a few dollars but has all the same food (in most cases)
-If you'll have a fridge in your room pick up some bottled water and freeze it overnight. As it melts it will stay cold and you won't have to constantly stop to buy drinks. When it's empty you can refill it.
Those are just a few, I'm sure others will add on. You can also google "Budget tips for Disney World" or "ways to save money at Disney World" and lots of sites will pop up.
Good luck!