D'Addario and Planet Waves have an excellent video on how to Restring a Guitar. It's great for both beginners and experienced players.
After changing your strings, it's common to have to retune it constantly. This only happens if something "gives." Often, it's the extra slack that is found in the 3 to 6 wraps that the string made around the tuning peg. As you play, the slack gives... and you're out of tune.
In the video, they do a lock wrap. (Put the string through the peg, wrap it back around and then under itself. When you turn the peg, the string will wrap over itself.) This is a lot like a clove hitch, one of the strongest basic knots. Because it holds the string so well, you can have fewer wraps. (I often don't even have a complete wrap on my bottom strings.) With fewer wraps, you have less slack. Your strings can be "broken in" in minutes rather than hours.
I've been stringing all my guitars this way (except the nylon-string guitar) for about 3 years now. I've even changed strings just before performing (usually not done because of constant retuning). It works great and I recommend it without reservation.
(a) I did try to embed the video... but I couldn't keep it from playing automatically.
(b) This didn't really work as well with nylon string (classical) guitars, for me. I think it's because the pegs have a larger diameter, the strings are a lot slicker, and the strings stretch so much. So, I haven't found any advantage to using this method with classical guitars.