Buy one of the laser alignment aids in golfsmith. This will insure that your putter grip is right on the money. You can be close these other ways (eyeballing & carpenter's square) and may even hit it just right on 1 out of 3...but the only 100% positive way to be absolutely sure all the time is the laser.
Take it to a professional club builder and let HIM do it...cheaper that way, and no hassle.
I wouldn't bet a pay check on that being true. I've seen more grips installed misaligned from custom club builders than I can count. Factory grips are just as bad, a lot of them are off a little as well. On most clubs it's not a big deal, with a putter or a club with a rib grip, it's a real problem some times.
I've re-gripped many a putter and have found that provided the putter head has an alignment line at right-angles to the face, AND the grip has a flat surface to the front, it is fairly easy to sight down the flat front of the grip to align it with the line on the putter head. If you check a putter before you buy it, it is surprising how many are off line (7 out of 10 peaople that read this will go and check their own putters and find they are off line also!! - and will no doubt blame this for the majority of missed putts). I putt with a fairly square (hand) grip but recall that Bernhard Langhar used to use a 3 or 4 degree closed grip and had his putter grips aligned accordingly.
I'm lucky I have a very sharp set of eyes and can pretty easily see that it's aligned, but I can't convey that obviously in words....sorry, not a help.
Place the putter in the vice and use a level on the putter face to make sure its perfectly vertical, install the grip, and then take that same level and make sure the 'paddle' is perfectly horizontal. Remove club and make any final adjustments at address.
If you are lucky to have tiles on your floor or a reference line use it after you have slid on the grip to line up the face of the putter and now hold the club naturally and see if it hangs parrallel to that line. you usually have 1-3 minutes to tweak the grip as it dries. Always try to align the "paddle" of the grip 90 degrees of the face as you slide the grip on.
This works only if your work bench or table is level. As soon as you slide the grip onto the putter shaft, lay the grip flat on the work bench. Then hold a level against the face of the putter head and tweak it until the level is vertical.