However, for a long time, I did not like the tails left behind on my serged edges. I didn't know what to do about them, because I knew they had to be left there so the stitches wouldn't come out, but they took away from my otherwise professional finish.
Anyway, here is this super-simple trick to get rid of those ugly tails! All you need is a yarn needle.
Thread the leftover tail through the eye of the needle.
Then, just clip off the tail at the point where it emerges from underneath the stitches and voila! You have a clean finish with no annoying tail.
Tip: The tail should just slide right under the other stitches. If you are having a hard time pulling the tail through the stitches, your threads are probably too "bunched up". Just grab the tail and ease the fullness out into a longer, thinner chain. In the picture below, you can see the part of the tail on the left has the loops of thread very close together and piled on top of each other. The right part of the chain has been smoothed out. You want your tail to look more like the side on the right before you feed it under the stitches.