When I first got in to bicycling, the standard method was to start taping near the stem and work your way outwards to the ends. Then stuff the end of the tape into the handlebar and secure it with the bar end plug. Of course, back then everyone used unpadded adhesive cotton tape, so it stuck no matter what you did.

This method probably won't work with the super-padded tape that all the out-of-shape kids use. The fat tape probably wouldn't fit in the end of the handlebar and/or would tear if you tried to secure it with the bar plug.