I agree with all the above answers, no device is required to stretch the strings. I use a couple of fingers to hold the string I'm stretching; for the thinnest strings I'll use a clean cloth as well, to spread the pressure of the string on my fingers.
Grip the string around the 12th to 15th fret and pull the string perpendicular away from the neck and body. If the guitar is laying on its back, you'll be pulling up; if in playing position, pull away from your body. I use the hand I'm not pulling with to make sure the string I'm stretching doesn't leave its slot in the nut. Also, remember to wipe the string clean after you're done stretching it.
I mostly play electric guitars, and I will stretch new strings extensively when installing them. I usually stretch metal acoustic guitar strings with less force on each stretch, but more passes of stretching and retuning. This is because I worry about putting extra tension perpendicular to the guitar top on acoustic guitars.
On electric guitars with tremolo systems, stretching one string will pull the bridge and lower the tension (and pitch) of all the other strings. I'm usually able to hold larger trem units (Floyd Rose and related designs) in place with my elbow while stretching the string, but not strat-style trem bridges. One can also block the bridge, or use some other method to hold it stationary while stretching one or more strings.
In any case, after stretching one string to the point where it stops losing pitch to the stretch, check the tuning of the rest of the strings. Even on a fixed bridge electric, they might have gone slightly out of tune. Tune them all up, and move on to the next string to be stretched.
After I get all my new strings stretched, I'll tend to play for several minutes, trying to bend notes on all the strings. Usually by this point they won't need any further stretching, but sometimes it can take several iterations to get a new string to settle in. Just keep stretching and playing until you're satisfied with how the new strings are holding their tune.