CP bottlers get their pressure from a CO2 source. They have a line from a pressurized keg of carbonated beer, and another gas line in. They also have a purge valve.
So you seal it to the bottle, open the CO2 in line, open the purge so that a blast of CO2 purges the bottle, close the purge, open the beer, then slowly open the purge so that the beer can fill the bottle. When the bottle is full, you close the purge, then close the beer in line and the CO2.
It takes some practice for sure, and it's basically impossible without a buddy to help (you gotta slap a cap on QUICK ). But they are great contraptions once you get the hang of it.
If your primary goal is saving time, I'm not sure a CP filler would really help. It's mostly so you can bottle force-carbonated beer.
Frankly, I'm done with counter pressure bottling. It's a total PITA and the results are marginal, at least in my case. I even went so far as to make a totally all stainless CPBF, and the results were still marginal. Mostly in regard to the beer changing in the bottle, not necessarily carbonation. Between loss of hop character in highly hopped beers to perceived oxidation after only a few weeks in the bottle, I was just never happy with the results. I've heard similar stories from others.
My solution? Fill from the tap. No special set up, no special equipment. Put a tube on the end of your faucet so you can fill from the bottom of the bottle up and minimize potential oxidation, sanitize, purge and chill your bottles, turn the pressure way down so you get a nice slow fill. Tap on the filled bottle to generate some foam to fill the last bit of head space, then cap on foam. I've had much better results with this and there is little to no clean up afterward.
I can't explain why this method gives better results for me. With the CPBF I still purged and capped on foam, but for some reason, the act of using that thing just didn't work like it should in theory. If you are planning to make or buy one, try the fill-from-the-tap method first and judge your results. It just might save some time and frustration.