This is a question we have seen a few times in sew a long groups. How do you finish a serger tail? There are many ways to do this. I'll show you several ways, including my personal favorite and you can choose which way works best for you.
Cut right against the seam:
This way does have the benefit of little to no additional work immediately. You literally cut the tail against the seam and be done with it. I personally will only do this if I have fabric glue to seal the ends down. Otherwise you run the risk of the threads unraveling.
Tie and knot against the seam and cut excess:
This way is nice, all you have to do is tie a knot as close to the seam as you can get and cut the excess off. This way does work well, but the knot can be bothersome to those with sensitive skin. It also can get pulled on or caught during washing and drying. I have only had a handful of knots come undone - usually through the picking of a certain older child of mine. You can use a single knot (left) or a double knot (right).
Tie each thread individually:
You can tie each thread individually as close as possible to the seam, then you cut the excess. I have never personally done this because it seems like a bit of extra work, with the same result.
Weave the tail under the serged edge:
This is my preferred method. I take a tiny crochet hook, wrap the tail around the hook and pull the thread under the serged edge. I then cut the excess. This way has never come undone and hasn't bothered my kids' skin at all.
Some use a large needle to weave under as well. I prefer the crochet hook because I already have them (i've crocheted for many years) and I'm less likely to get frustrated trying to thread the needle.
Sew over it:
You pull the serger tail back a bit from the edge and sew it down either by hand or using your sewing machine. The type of stitch you use depends on the fabric. Straight stitch for woven and a stretch stitch or zigzag for knits.
Leave the tail:
Leave the tail long and ignore it. I don't like this way, but I know it has happened when my kids run off with something before I finish the tail. It can be pulled during a washing cycle, but I don't think there is necessarily anything wrong with leaving this unfinished. I wouldn't recommend selling items with an unfinished tail.