I re-read that entire article again after I posted the link, and although it gives a lot of semi-technical info about the process it is somewhat light on specific procedure.
It seems that the whole idea has been somewhat over-dramatized in tape recorder lore in that it has to be done a lot, and if you do it at all wrong you will make matters worse.
Jay's article seems to debunk some of the more commonly held myths.
As to exactly how I demagnetize (feel free to correct me here fellow Tape Project experts), I turn on the unit about 3 feet from the recorder, move in fairly rapidly and touch each metal part (heads, guides, capstan etc.) with the protected tip of the demagnetizer and move a few inches away fairly slowly at first, in a circular motion, then back in for the next part etc., NEVER turning off the demagnetizer near anything. When I have covered all pieces, I typically move back in fairly close to the center of the whole general headblock area without touching anything and then out again in increasing diameter circles as I had for each individual part, till I am about 3' away or however far I can reach and/or the cord will let me go before turning off the demagnetizer. The main thing is to not turn the demagnetizer power on and off close to the heads or other parts, and to get close enough to each part and not jerk the demagnetizer rapidly away at first from the part. As you get further away how smoothly you move becomes less critical. Of course you also don't want to actually scratch the heads with an unprotected metal tip.