I`m sure Accumulator will chime in here eventually..
I learned about the foamgun from (the now-MIA) YoSteve.
It took me quite a while (countless washes over a long period of time...and I don`t mean "a few months") to get my routine squared away, but now I can`t imagine ever washing without it. I`ve probably tried *every* foamgun-centric approach imaginable (and I have quite the imagination

).
I need to write this up properly some time, but here`s the thumbnail-sketch version:
(Regulars here might notice some changes if they suffer through reading the whole thing.)
I mix up gallons of shampoo concentrate at ~7oz. shampoo + enough water to make a gallon. I fill the foamgun with that (I keep extra foamgun canisters full of concentrate handy). (Note that this same concentrate works well for cleaning LSPed wheels and the wheelwells/undercarriage.) I use a *LOT* of this shampoo mix so I keep a few gallons in old shampoo jugs.
I use the three strongest foamgun settings, varying between them as conditions warrant.
This rate of shampoo consumption and water use will disqualify my approach for many people but isn`t a problem for me.
I find presoaking with the foamgun to be of limited value. I basically only do it so there`s shampoo mix on the panel before I touch it with anything, although the extended dwell-time probably contributes something.
IME, mechanical agitation is necessary to get things clean. I use a BHB to get the "big stuff" off, but when used properly that`s too gentle to get "road film" off so I usually follow up with a mitt.
I do at least two phases, both with constant spraying of foamgun output at the point of wash medium-to-paint contact. First I use a Boar`s Hair Brush ("BHB") then I follow up with a mitt. On *very* rare occasions I`ll do a Garry Dean Wash Method rinseless wash after the BHB step, but I usually don`t do that until I`ve also do the mitt step (if I do it at all). I often do all three.
The basic idea is "dislodge and flush"- the constant stream of foamgun output flushes the dirt away as soon as the wash medium dislodges it. That way very little dirt gets stuck in the BHB/mitt (which would drag it across the paint under pressure, causing marring). If a BHB or mitt is touching the paint, the foamgun is spraying its output at the point of contact.
One hand holds the foamgun, the other hand holds wash medium. They are moved in tandem so the foamgun is always spraying output at the point of wash medium-to-paint contact (and I try to move the foamgun so that it soaks the entire BHB, which is longer than a mitt). There`s an element of "rub stomach/pat head" involved, but it became second-nature after a few dozen washes.
Wash media are always moved in in straight, short, interrupted "jiggling" motions, *NEVER* long, sweeping motions. The straight motions keep any marring that does occur linear (and thus less obvious than elliptical/circular scratches are), short motions keep any marring short rather than long, and the interrupted jiggling motions make it easier for the foamgun output to flush the medium clean while in-use rather than allowing it to get loaded up with dirt.
Steps:
-Rinse vehicle off, preferably with pressure washer
-Spray foamgun output on panel(s)
-Dunk BHB in wash solution bucket
-Spray foamgun output onto BHB to further prime it with shampoo mix
-Move BHB across panel, while spraying foamgun output at point of BHB-to-paint contact
-Rinse panel (either with hose or with foamgun on "clear water" setting, which is also good for rinsing jambs/etc.)
-Inspect, repeat if panel still appears unclean
-Dunk washmitt in shampoo bucket and/or fill it with foamgun output
-Hold mitt shut at cuff and spray foamgun output on its outside to further prime it with shampoo mix
-Gently whisk across panel while spraying foamgun output at point of mitt-to-paint contact
-Stop and refill mitt if shampoo seeps out before I finish area being cleaned
-Rinse panel
-Inspect, repeat as needed
This is all *MUCH* easier when the foamgun`s pistol-grip is replaced with a 90° shutoff, which I operate with my thumb.
The foamgun will often/usually rinse the BHB clean while washing (perhaps because of my boosted water pressure, might not work for everybody), so I probably don`t need to dunk it in the rinse bucket (and the reprime it with shampoo mix) as much as I do. The mitts don`t rinse out as well as the BHB so I always rinse them in the bucket and reprime them, but this might also be unnecessary as the rinse bucket hardly *ever* has any dirt in it at the end of the wash. The shampoo bucket stays clean enough that I usually just replenish it rather than dump it out.
Not the right approach for everybody, but it`s virtually eliminated wash-induced marring for me; I basically don`t need to polish any more even on daily-drivers that get used hard year-round.