I know of three ways to do this:
1. Leave a tail at each end, then thread them onto a large-eye hand sewing needle and pass the tails back through the seam.
2. Cut the tails and use fray check or similar product to secure the end so the threads don't come undone.
3. After taking the first stitch in the fabric, take the tail, bring it to the front of the needles, and serge over it. That will take care of the first edge. Then at the end of the seam, take one stitch off the fabric, flip the fabric to the front of the foot(without cutting the threads), and gradually serge off the edge of the seam. You will be serging over the last inch or two of the seam, so be careful to avoid the knife...you do not want to cut the previous stitching.
Hope this helps.