First, you can do it with your fingers. In fact, a number of top notch stringers do just that. The reason some use the setting off awl is if you're stringing a ton of frames, particularly in these times of poly and shaped strings, your fingers can get sore. The awl, after some experience, can be as effective and quicker. While using it, it is a bit of a stabbing motion but that's just the angle you use to get leverage to move the string--the awl tip does not hit the top of the string--it goes into the space at an angle, providing a glancing nudge to move the string. Keep in mind that, irrespective of whether you use your fingers or the awl, if you've kept your strings mostly straight while weaving/tensioning, these are just small adjustments--the finishing touch, if you will.
I'm not sure I've seen a video tutorial on the technique, but Richard Parnell's video of the Wimbledon stringing room last summer (do a search on You Tube) shows a stringer or two using the awl technique (and a few just using their fingers). If you decide to get a setting off awl, start off slowly or you will surely damage the strings. The pro stringers who have perfected the "Norman Bates" technique have years of practice on thousands of racquets.
