Let's break this down.

As /u/Natejitsu said, you use the solvent right after shooting (yes it can wait until you get back home, but don't wait until the next day.) If you don't have solvent, Windex does the trick just about right. Windex contains ammonia which neutralizes the corrosive leftover from the Berdan or other surplus primers.

From my experience, you can forget about RemOil. It does shit all to preserve your rifle. Get Hoppe's gun oil (the viscous clear type) or some really high viscosity engine oil (MUCH cheaper and it will last a lifetime). Forget the bore snake, get a proper rod (bronze or carbon fiber!), a .30 cal bronze brush, a jag and a patch head. (You could also use the cleaning kit that came with the rifle.) Ideally you should also use a muzzle protector. The cleaning kit that came with the rifle has one - it's the cap of the cartridge.

Soak your bronze brush in solvent, run it a couple times through the barrel, push the jag 2-3 times with patches then clean with a dry patch. Repeat. Then use the patch head and run a patch soaked in oil through the barrel.

For cleaning the bolt carrier, bolt and chamber, search YouTube. There are plenty of how-to videos. Basically the same order applies: solvent first, dry clean, then oil. Don't forget to clean and lubricate the recoil spring. Also make sure the piston and gas tube are coated in a very light coat of oil. They have a habit of rusting from corrosive residue. Ditto for the gas port (use a q-tip to clean that).

As for storage and firing - f you store your SKS for a long(er) time, leave it "wet" (as in, soaked in oil.) Prior to firing it, clean it with a dry patch (bolt, chamber, receiver) and run a clean snake through the barrel.

This about concludes the free lesson on field cleaning your SKS. You're welcome.