I think the most important thing to do is think long and hard about what is important to you on vacation. You don't want to cut costs EVERYWHERE or it's hardly a vacation at all. Decide what is worth splurging on to ensure that you really enjoy your trip, and then look for the cost savings where it doesn't matter so much to you.
For instance, FOOD. For some people, dining at Disney is one of the things they look forward to most. They book character meals, get all their ADRs 6 months in advance and determine which park to visit each day based on where they want to eat. On the other hand, you have my family. We need to eat, but with the exception of a few select Disney snacks (my husband would hop to EPCOT just to get a Cronut) we don't care where or when. We don't make any ADRs and most of the time, we ALL order kids meals. Many people don't know, but if you're not on the dining plan, adults can order kids meals at any quick service restaurant. At Pinocchio Village Haus in MK, you can get a cheese flatbread for $11.99. The kids meal for $6.99 comes with half a flatbread, but also includes a yogurt smoothie, some fruit (applesauce, packaged grapes, etc.) and a drink. The drinks being included with kids meals is one thing that really tips the scales in my opinion, if you don't want to drink free ice water all day.
Souvenirs. Lots of people talk about buying them in advance so you have something to give to your kids each day. For our family, we talked about expectations beforehand. We explained to the kids that there were going to be stores EVERYWHERE selling things, and they would need to be really smart. They did chores around the house to earn "Disney Dollars" before the trip (ended up being between $30-50 each) and at the parks, they knew that was all the money they had to spend. We also encouraged them to wait until the end of the trip to actually buy anything, to make sure they were getting what they wanted most. (By the way, our kids were 4, 6 and 8 that first trip.)
If you are getting a rental car, make sure you keep checking rates after you book. Some great deals can be found just before your trip. Just cancel and re-book at the lower rate.
When choosing accommodations, you have to really do a detailed cost analysis to figure out the best deal. For our family of 5, off-site always makes more sense. By booking a condo or townhouse, we get more room for less money and save loads on food by making some of our own meals. But we need to add on the rental car and parking costs ($25/day at the parks) and that adds up quick. If we had a family of four, it would be a much tougher decision.
Finally, if you really need/want to save money, avoid the "extra" events. You don't need to go to a dessert party to see the fireworks. You don't need to do Early Morning Magic to get on SDMT. A lot of those options may enhance your overall experience (I wouldn't know), but they certainly aren't necessary.