I bottle from the tap pretty regularly, and without a specialized device. Assuming the beer is carb'd:
1.Turn off the gas to the keg in question.
2. Bleed nearly all the pressure out of the keg, leaving just enough to flow. "Bump" gas back in as needed to flow.
3. Slip 1/2" I?D tubing (~8" long) over outlet of nozzle
4. Put tubing in bottle/ growler.
5. Keeping the vessel at a steep angle, almost flat, open the tap. I tend to keep the outlet of the tubing near the mouth of the vessel until there's substantial liquid in the vessel. Then, I submerge the end of the tubing in the beer.
6. When full, turn off the tap. The first bottle or so will sometimes be too foamy (a neck's worth of foam). Either fill the rest and come back to it or, if I'll be the drinker, suck the foam off and continue filling.
7. Cap.
8. Remove tubing, clean it- sometimes, hehe- and turn the gas on to the keg.
Mine isn't a fast process and I've done it enough that I can read my flow which makes it much, much easier. I've done this for immediate consumption as well as long-term storage. The key to long-term, and I'm talking anywhere from a week to 3 years, is bottle sanitation. If I'm drinking the bottles tomorrow I won't sanitize them but if they'll be stored for more than a couple days they can cleaned and sanitized. Kyle