There are many different methods out there on how to string a guitar. I'm sure a lot of them work fine. There's one method I've learned that is the simplest and most effective method I have seen, that doesn't require pointless wrapping and wrapping of the sometimes too short strings around the tuner for it to work.
The basis of this is taking the string, and trapping it tautly under itself when you turn the tuner tab, trapping it in place.
First off I recommend after removing your old strings, to give your guitar a good cleaning as it can build up dust and gunk in little nooks and crannies that are unreachable when the strings are mounted. Once this is done set the tuner pin (as I will refer to it as; the vertical pin that has the hole in it to put the string through) parallel with the guitar neck.
Place the string through the tuner pin. Grab the excess that is sticking out the end of the head of the guitar tautly, and pull it around a full 180 degrees towards the inside of the guitar so that it is now through the loop, pulled towards the inside of the guitar, and facing down.
Now, make sure that when you do this next part that you keep the excess string on the top. Take the string that is now facing down, put it under the taut string and pull it back up a full 180 so it is now facing upwards again. What this will do is create a loop around the tuner pin and under the string. Turn the tuner knob towards the outside of the guitar (the opposite way you turned the string) and this will tighten the string and trap the excess under it.
Tighten the string to its proper tuning and rinse and repeat. That is how to string a guitar in a simple and effective method