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First, you will need a safety pin to pin on the end of your piece of elastic.
Then begin to thread in your elastic by placing the pin end in first.
Pull some forward and then pull your cloth back towards the other end so that you will have room to pull the pin forward and scrunch it up again. Keep doing this until the end (non-pin end) is at the very edge.
Here's a picture of the Diaper Bag that I finished making today for my sweet daughter, Heather.
PS: If you would like to see the tutorial that I used to make this great bag go here to Sew Much Ado