As with any organization project I do around my home, I take everything out of the space I'm organizing and start with a totally clean slate. It's easier to fill up an empty space in an organized way than to try to shift around what's there.
With all of your games out in the middle of the floor, start grouping the boxes together by size. This is especially important if you ordered various sizes of file bags.
The best part of this whole process is throwing out those broken, old, cardboard game boxes! Start matching your game groups with bag sizes. I simply laid the boxes on top of the bag to do a quick check for fit.