I think the basic rule is
if possible to be patient when attacking with the Russians and wear down your opponents units over a number of turns, move MG and Field gun units to within two hex's and fire at the target hex over a number of turns, if you can use a higher elevation to fire "over their heads" that is even better, obviously if you can add arty hits to the attack that will be a bonus.
Sacrifice
one battalion to move adjacent to the target hex to add to the fire, never have more than one battalion adjacent until the moment of the assault as this will incur heavy losses/fatigue, hopefully in the end (might take one turn or multiple turns) you should disrupt the infantry unit accompanying the MG unit, then you can soak up some of the defensive fire with your MG/FG units and then using a stack that you have kept hidden behind the "sacrifice" battalion assault the hex.
Obviously luck plays a role here and sometimes the MG unit will deliver defensive fire and sometimes not, if the units in your stack are disrupted don't leave them adjacent but move them back out of LOS if possible to avoid heavy losses and fatigue.
Remember not to wait for your opponents MG/FG units to disrupt as this rarely happens, as long as the accompanying infantry is disrupted you are good to go.
Unfortunately the process requires practise and knowing just when to assault is a black art in itself and even if all goes well the "die roll" might go against you and you don't take the hex.
The strength of the Russians is their numbers and generally you can wear the CP forces down over a number of turns introducing fresh troops to the attack, the CP player cannot have FG/MG units everywhere so try to attack in places where they are not located, but patience is the key which does not come naturally to me so I also went through the same learning curve when I started with the FWWC series, I remember my frustration back then and Ed (Volcano Man) giving me very similar advice to what I am doing for you now!