"Clean like you would anything you'd make and server food with"

For me, that means rinsing and wiping the basket dry after every shot. I rinse the group screen (or BPlus) after every shot (into a cup, so I don't have to empty the drip tray as often) and use a washcloth to wipe the excess water off the screen (so it doesn't drip onto the puck when I lock the PF in).

At two shots a day or so, I soak what is easily removable on my machine (basket, screen, dispersion block on a DE1, BPlus screen, steam tip) in Cafiza (or similar) weekly. After the soak, I rinse well with clean water. I scrub the group gasket with a stiff brush and Cafiza solution. I have used the Pallo Coffeetool Group Brush for many years. There are probably other, similar brushes as well.

On a conventional machine, the brew path is shared with the exhaust path. These machines can benefit from backflushing with a blind basket and Cafiza periodically. I'd guess somewhere between monthly and weekly for a typical home user, depending on how many shots you pull a day. If you wait too long and the exhaust is really grimy looking, you might want to go more often. When you backflush, you also tend to remove the coffee oils from the cam inside the E61 group. That can lead to squeaking sounds until they build up a bit again.