Lately, I have been using a method that I read that Jimi Hendrix used to stretch his strings. Originally, I was using it for Strat's with tremolo bridges, where any little tip can be useful to help with tuning problems. Now, I've found that it can help with stability on all instruments with new strings.
Place the string in/through to bridge and secure. Holding the guitar to keep it from moving (I was using my left hand on the headstock in the photo) pull the string, starting at the bridge, while slowly moving down the string toward the other end until you reach the end. Do this several times for each string before you attach to the tuner and tune up. You may want to use gloves.
Hendrix believed that this was a better method than stretching the strings while tuning, as the winds on the strings can be difficult to initially loosen while tuning and this is more likely to happen while playing. You will still need to do some stretching while tuning in order to get a good seating at the bridge and tuners.