Anybody complaining about tuning stability on their guitar, I guarantee they did not do this step when changing strings. There is absolutely no reason for new strings to constantly go out of tune if you do this.
Every time you change strings, they need to be streched. Tune them up to pitch, take each string with your fingers as shown in the image on the left, and strech it by pressing with your thumb the whole length of the string, from the nut to the bridge. Repeat for all six strings. Retune – repeat – retune. After this your strings will stay in tune a lot better.
There are even tools designed for this purpose, but in my opinion there is no need to buy them as you can do this with your hands only.