Depending on how much you shot, you might not need to clean it at all. Many of mine will go to the range at least 4 times before I clean them. The rifle's design is traditional Russian military and will function flawlessly even when filthy inside and out.
I do know a few people that clean theirs after every trip and there are a handful of choice SKS rifles I own that get cleaned after firing them.
As far as a standard cleaning, just take the receiver cover off, remove the recoil spring assembly, pull the bolt assembly and carrier back and remove. That allows you to use a standard cleaning rod from the receiver end.
Depending on how dirty the bore is, I usually run a wet patch soaked with Break Free CLP through the bore a few times, let it work for a minute or two, then run a .30 cal brush a few times and then a few more patches soaked with Break Free to clean up. Then I use a few dry ones to get any oil residue out of the bore.
Its a good idea to wipe the bolt face to get any build up off and out of the extractor. Then an overall wipe down of metal surfaces with a rag lightly sprayed with Break Free. This is recomended especially for any areas that have corrosion like your magazine or any areas that have worn bluing.
You can clean the gas tube if you want but unless you're shooting corrosive military ammo you don't have to for a long time. There is a tool for scraping carbon out of the gas port in the barrel but a bent Q tip with most of the cotton removed will often get in there just as well.
If you haven't shot many rounds through it, the easiest way to keep an SKS clean is to give the bore a light spray of Break Free from the receiver and run a .30 cal Bore Snake through it. These work great for clean bores that have seen a few rounds here and there.