I keep coming across instructions which say to either fray stop the cut edges of overlocking/serging, or to weaving it back in with a needle. I am not a fan of either method so would like to propose a third method, which is nothing new, but I thought it might be useful to do a mini tutorial.
This all happens on the overlocker and it is useful to practice on scraps because you will become adept very quickly. Before I begin let me mention that it is really difficult to show the method in photographs but I’m going to give it a go.
You will have a tail at the beginning of the seam and you want to overlock this tail into the seam: Do a couple of stitches into the seam with the tail at the back as normal (use your handwheel if you need more control), leave the needles down to anchor the fabric and raise the presser foot. Bring the tail to the left side, smooth it out, and pull it underneath the presser foot. Drop the presser foot (how useful would a knee lift be?) and continue overlocking, letting the blade slice through the tail after a couple of centimetres. This end of the overlocking is now anchored into your sewing.
At the end of the seam, overlock one stitch off the end of your fabric. Raise the presser foot and needles, pull the fabric out so that the thread comes off the stitch fingers – I’ve tried to show this here, but it’s a bit unclear. If you don’t know what the stitch fingers are, either check your manual, or just look to see that they help form the overlock stitches. They are fairly obvious when you look.
Now flip the fabric over and reposition it under the presser foot. You are going to overlock back over your previous overlocking. I am careful not to cut my previous stitches, but if in doubt, disengage your blade so there can be no danger. 
Overlock a few centimetres and then off to the side. You can now trim the overlocking – it’s not going anywhere. Can you see the beginning and end of my overlocking on each seam? If you want it to be a bit neater where you chain off the end just pivot the fabric more. 
I also overlock around the corners by stopping a stitch after the end, lift the presser foot, lift the needles, pull the thread off the fingers, turn the fabric 90°, gently pull up any threads to remove slack, and then keep going. This is another skill to get practiced at.
I made a bundle of these little bags recently to give away with soaps in them, and each one took literally a minute including cutting out. Had I been fray stopping or sewing the tails back in I think it might have taken me a fair bit longer.
What method do you use? Anything to add?