Basic stuff... Use the tire tool as little as possible. I only use it to dismount the tire, and then only to get it started. I can wrestle most any tire on without tools.
Try to find the leak before removing the tire. Look for that piece of glass, tack, nail, wire, etc. in the tire.
Once the tube is out and you find the leak or hole, mark it with a pen.
If you're repairing, use good quality rubber-cement patches. Properly applied, they are nearly as strong as the original tube.
Before putting the tube back in, go over the interior of the tire thoroughly. Sometimes, the tiny wire piece or thorn or whatever will be invisible from the outside. An old trick is to run a fuzzy cloth (an old towel works well) around the inside of the tire to see if it catches anywhere.
Before putting the tube back in, re-inflate it just enough to get the wrinkles out and let it hold a bit of shape.
This also prevents "pinching' the tube between tire and rim.
Not a bad idea to check your rim as well to see if any spokes are poking through the rim strip.
Re-inflate carefully, making sure that the tire's bead is seated properly.
Use a good floor pump with a pressure gauge.
An annoying flat-causer I've been encountering more and more is tiny bits of steel-belt tire material. Short, tiny pieces of wire that are very hard to spot.