It is my understanding that in the prone position you are supposed to lean into the rifle so as to put forward pressure on the bipod. However, I also read that you are supposed to be using your left hand to pull the stock rearward into your shoulder. Are these both correct? How can you exert pressure forward and backward at the same time?

You aren't pulling on the toe of the stock as much as you are simply holding it to your shoulder. The less input you give with that hand the better.

Crow King wrote:How can you exert pressure forward and backward at the same time?

Your shoulder is pushing forward on the stock.
Your hand is pulling rearward with less force than your shoulder is pushing forward with.
If you watch the snipershide video, Frank shows how you pick up your body and the rifle together so that the bipod legs slide back a bit, then you go back into prone and there will be some natural force between the bipod and your shoulder.
You should not be making an effort to actually push forward with your shoulder as they would distort your prone position.

I wish it was that easy for me to transition to support side/weak side. I cannot get a sight picture at all in the weak side... Would probably have to pull me stock pack off because I feel like its too tall..... I knew I had a crooked face....