Two thoughts. The lady that was leading our knitting group suggested we use needle-nosed pliers to poke the holes through, and then clasp the end of the handle, and pull it back through...worked like a charm!
As to how you do it, we had about 6 of us working on it at the same time, and came up with about 6 different ways to do the handles!
I folded the bag the way it said, but ended up putting one end of the handle through one side (one "fold") and the other through the other side ("fold") and tying it in the middle (of the side of the bag). Then I did the other side of the bag the same way. (I hope that makes sense...it was clear when I did it!
Others just skipped the folding thing, and put the handles where they wanted them and knotted them on the inside of the bag.
*Okay, I looked at the picture
again, and where it show how to poke the needles through, it's folded so you go through 4 layers. I put the handle (if looking at the picture) through the top two layers from the, and through the bottom two layers from the bottom, and knotted it between. (Man! It's so much easier to show in person than to describe in words!!!!)