After the shot, I do a quick 6-7 second flush. Then I rinse the screen and the entire area including the gasket with a laboratory squeeze bottle. I fold a small sheet of thick paper towel into a wedge, and run it around the interior of the group (reaching up with it toward the gasket).
I do a water back flush after every shot (they are usually not back to back shots, and I'm not always sure if I will be having a second or third, oftentimes it ends up just being one).
I do the chemical backflush when prompted typically, but sometimes more often if I happen to be doing other general tasks. I clean the drip tray after the chemical cycle, and I repeat the cleaning cycle until I don't see any coffee-gunk in the drip tray. Before I started the per shot flush/rinse/wipe/back-flush, I would have to run 6-8 cleaning cycles to get clear water in the drip tray. Now it only takes 2 or 3.
I installed an IMS screen, and when I took the oem screen off, I expected to see a lot of crud as I don't often remove the screen, and for this BDB I'm sure it had been over a year. Both the screen and the mount were spotless. I attribute this to the process I describe -- in years past, when not doing that process, it was an unpleasant mess.
Side note, I used the IMS screen but didn't like it. So after two shots (each with the flush/rinse/wipe/back-flush), I pulled the IMS screen off: it was covered in coffee fines on the inside surface: they didn't flush back out thru the screen (low pressure flush) nor did they get picked up by one black flush. So using the IMS screen may warrant more frequent removal/inspection/cleaning for some users.