Me and a friend of mine play this a lot and we had to explain it a bit to a new player, so we also had to give the USSR an advantage because it would be first time player against a veteran.  
We found that there are three ways to make this a bit more fair:

 1. Give the USSR more starting influence to divide (this can be in Eastern Europe or in any other continent)
 2. Give the USSR some starting points, that way America has to accumulate more points to win the game, I think that 5 or 3 is fair but you can choose that for yourself
 3. In the first headline phase: USSR plays a card and America doesn't, this can give the USSR an advantage if they have good cards so it's a gamble.