Something must be wrong either with your guitar or the way you are stringing and tuning the string.
Firstly, use a tuner. It's more accurate. In my personal experience, I always tune the high E very slowly. When you use the tuner, you can see the string slowly getting into tune. That way you can know how much force to be applied to the tuning keys.
When stringing, coil around the tuning head neatly and avoid overlapping the coils. Generally, you don't start stringing from the beginning of the string. Pull in about 100mm or 6" or so before you start stringing and cut away the excess after you're have tuned the string. Look at how guitars are strung when you visit a music shop and remember how they look like. This will give you an idea of how it should be.
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