Tim's restring technique
There is no exact or best technique for restringing the guitar. Over the years of stringing my own, friends and customers guitars, I find this technique works best for me. It reduces excess string around the machine head and the "string pinch" both contribute to reducing the risk of slip and going out of tune.
Always use a decent brand of string as cheap and nasty strings can cause more issues than the "money you save" is worth.
Firstly loosen off your strings
When you have no real tension on your strings cut them off and throw them out. Some people think it's a good idea to keep them as spares. Just remember there is a reason why you are changing them.
Check your string packet for a reference to which string is which. This may seem a bit trivial but we all get absent minded from time to time. Even the best of us have popped that B in the E position once in our lives.
Thread the strings through your bridge till the ball is sitting agains the hole you fed it through. Bridges can vary, this is an interesting style on the Hagstrom so I have included an image of "tune-O-matic" style also. Some guitars are threaded through the body.
This is where people can vary in technique, here I will show you the way I find works well for me. It can take a little practice getting used to the hand positioning but when perfected makes restringing a breeze. Insert the string through the machine head from the outside of the headstock. You want a little slack but not too much. The exact amount comes down to feel and a bit of trial and error.
Pull the string from the outside over the top of the machine head pole to the inside.
This will loop over the loose side of the string when you start winding.
Use your index finger to hold the part of the string closest to the machine head down while using your pinky to keep the tension on the string. This will ensure the wind around the machine head is firm and does not form any loose sections.
Keeping the tension on the string start winding the machine head.
When the other side of the string that is hanging loose comes back around make sure the part of this loop goes underneath the loose string. This will get the string loops to pinch on the threaded string reducing the risk of string slip.
Repeat above on all strings. Images below illustrate bass string thread and loop over technique.
Tune your guitar as you normally would.
Cut off excess string.