Unexpected hiccups can mean additional costs, so stay on top of your construction schedule. If you're sourcing any materials yourself, have them on-site when your contractor needs them.
Make sure you know what areas of your house need to be clear of furniture and take care of that before workers arrive. It's not cost-effective to pay expensive workers to stand around while you clear dishes out of your kitchen so that they can cut a new window in the wall.
For a larger renovation, you may have to stay in a hotel during certain parts of the process. Book that room well in advance to save money.
Keep track of any special requests that you made. While we painted our addition ourselves, we did pay the contractors to prime the walls and paint the ceilings. The day that the painters arrived, I randomly asked to see the low VOC paint and primer that we'd requested and paid extra for. It turned out that there had been a mixup, and they had to head back to the store. If you have special requests like this, especially ones that cost more, don't let that money go down the drain!
Staying organized also means keeping up with any paperwork and staying on top of your contractor, if necessary. If your contractor is responsible for pulling permits, make sure you know what's due and when, so you can check to see that everything is properly permitted. If your city slaps you with a stop work order, you can face costly delays in the project and possibly fines.