You do need to use a car shampoo. Part of it's job is to help remove the dirt.. either by helping to dissolve it or by clingining to it and making it softer, and lifting it off the paint... but it also lubricates the grit particles as you wipe them off with your mitt. If you use a sponge particularly and no shampoo the grit in the sponge gets dragged across the paint surface and will mark it over time.
Having said that, don't get tooooo hung up in the sponge vs mitt. The most important thing is that the beast is spotless. Use 2 buckets.. one with the soapy water and another (clean warm water) just to rinse the sponge/mitt in before you dip it back into the soapy bucket. If you have a sponge.. at this point just rinse it more than seems natural and check the face is clean... you have to be pretty obsessive).
Also your sponge/mitt is not a scouring pad. It's to remove dust, grit and dirt that comes off by wiping it. If anything else is left on the surface.. don't get hung up on it. Just leave it for the moment.
Rinse the car. Using snow foam helps the water cling to the car.. softening and lifting the dirt... but it's not essential. You can introduce that into your routine later.
Wash the car with your 2 (shampoo and sponge/mitt rinsing) buckets
Rinse the car.. using clean water. De-ionised may be good if you wash the car in sunlight or you have particularly hard water. Try to wash in the shade if possible.
Dry the car. Again.. chamois has its detractors but only people who don't keep it obsessively clean.. Use a micro-fibre towel for the time being if you want to avoid controversy on the forum
Don't scrub it.. you only want to get the water off.
Have a cuppa. That lets the car finish drying naturally.
Get yourself a clay kit and veeeeey gently just go back to those marks and lumps of dirt that didn't come off when you washed it. Use a fair bit of the lubricant and wipe it with the same amount of pressure that you might use to write. Failing that.. if the marks are "tar" (on the sides of the doors usually) then dab some paraffin onto a clean cloth and wipe it off. Be careful though. Clean cloth can mark the paint... You're not rubbing the tar off, you're dissolving it.. so that should tell you how much pressure to use (i.e. hardly none).
Your paint is probably a bit streaky now. You want some glaze and some wax.
Etna black was invented for Poorboys Black Hole glaze (some say it was the other way round). This is neither a polish or a wax.. (it's a glaze) so you're not rubbing it on.. you're smoothing it over the surface. You need an applicator pad. Apply it all over.. let it dry and then microfibre towel it off. Your paint should look pretty saucy now.
Wax the beast with your favourite wax. Autoglym Super Resin Polish etc. is not a wax.. You need a pukka wax, not a combined (polish-filler) product .. otherwise you'll remove that glaze you just put on. Try Poorboys Natty Blue since it smells of bubble gum.. but there's a million products out there with a fan-club.
Apply it with an applicator. Meguiars sell an applicator twin-pack. How handy is that?
While that's curing ... do your wheels and tyres since they'll look minging now compared to the paint. Wheels.. you can wipe off the water spots and leave them.. or use a wheel wax/sealant on them to keep them shiny. Essentially it's a tougher version of "wax".. Again, there are plenty of recommendations to be found but "Rim wax" seems popular (can't remember who makes it...
) I use the same wax I used on the body.. since I always forget to buy wheel wax when the old one runs out..
Finally.. get your towel out and buff off the body wax. Your car should look like someone swapped it for a new one when you weren't looking.. Have another cup of tea while you admire the view.
Rinse (actually wash) your sponge/mitt.. chamois... and any applicators that look a bit dirty (they shouldn't do, logically). I use the soapy water left in the wash bucket (not the black water in the rinse bucket) and then give them a final rinse under a tap. You really want these to be immaculately clean for next time. Leave somewhere clean to dry.. put them away somewhere safe until next time (i.e. not on the garage floor).