The attorney files a one-page entry of appearance electronically with the court e-file system, and then writes a letter or email to the prosecutor asking for a non-point disposition. 99% of the time, unless it's a severe speeding charge or something like a DUI or reckless driving, the prosecutor will issue a revised ticket for something that doesn't show up as points, but has a higher fine attached to it.
For example, if I got a 15 mph speeding ticket that was going to be $190 and two points, if I went through the process, I'd likely end up with a defective equipment ticket (non-point) and a $250 fine.
I've pretty much stopped handling traffic tickets because I don't like doing high-volume, low per-client pay, practice areas. But I did quite a bit of it when I was a younger attorney. It takes about 5 minutes to process the paperwork for the client to get the recommendation from the prosecutor.