Basic things:
1. Do you know how to build new units? (I don't mean replacements). It seems you already do, but it's worth pointing it out. Lotta people played this game for quite a while without having a clue.
2. The key in AGEOD games is (in my humble opinion) national morale. Unfortunately in RUS, Red morale plummets quickly if they're the AI, so you're likely to do well. What is the national morale of you and of the reds in the last page of the ledger (F9, i think) ?
3. Supply-supply-supply. Carry 3 or 4 of those with you. Armies are *a lot bigger* than in any other Ageod game. I had 180,000 (!) soldiers as the Southern Whites and was on my way to Moscow when Stalin (200,000 soldiers) and Trotsky (180,000) (!!!) hit me from the front and back simultaneously. Pretty much game over.
4. Needless to say, don't move in the winter into areas that don't have structures. Better still, find a city for each army corps and stay there. Russia is ... cold. And deadly.
5. Pay attention to regional limitations. There are only a handful of units or so that you can build and that can fight *anywhere* in Russia.
6. The reds have several heavyweights: Voroshilov sticks to my mind, although there are a few others. Pay attention to battle reports, to see if they've died

(if they died, there's a cross next to the box which shows how many stars they have... or "had").
I'm not spoiling anything for you, these things are pretty basic, but I hope they'll help.