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Stretch the String To Help Maintain Tuning
After bringing the string into approximate tune, gently pull up on the string for several seconds, and then re-tune the string. Continue until the string no longer goes out of tune.
Although the string has now been brought into approximate tune, you'll find that pitch will be hard to maintain, unless you take a moment to stretch out the string. Grab the string somewhere over the sound-hole, and gently pull upwards for several seconds. The pitch of the string will drop. Take a moment to re-tune the string. Repeat this several times.
Finally, use a pair of wire cutters (or an equivalent) to trim the excess string. Snip off the end of the string protruding from the tuning peg. Try and leave about 1/4" of string remaining.
Congratulations, you've just changed the sixth string of your guitar. It may have taken you a while, but with practice, you'll be able to change a string in under a minute.