I've been asked how to do this by a few people so I thought it was about time I took a few pictures and made up a tutorial. Overlockers are great for seams, especially on knits, but if you don't secure your threads, they can come undone.
There are a few different ways of doing this, one of which is to thread your chain through a needle and then work it through your stitches. That sounds too hard to me! I like the method below because the seams are finished as you are serging/overlocking so you don't need to do anything later.
To Secure the Threads at the Start of a Serged/Overlocked Seam
To start with, you should have a bit of a chain coming from the machine. Put in your fabric and sew a few stitches. Stop, making sure the needles are down. (I have taken my presser foot off so you can see what I'm talking about.)
Raise the presser foot and gently tug on the thread chain to stretch it out. Pull the thread chain to the left, around the left side of the needles and under the presser foot.
Above is the same picture, but with the presser foot back on. Lower the presser foot and sew about 1 inch, while holding the thread chain forward. Then pull the thread chain over to the right so that the knife will chop it off. Keep stitching.
Above you can see what the secured threads look like at the start of your seam! They are nicely locked in and not going anywhere.
To Secure the Threads at the End of a Serged/Overlocked Seam
Serge to the end of your fabric and then go one stitch off the end of the seam.
Raise the needles and the presser foot. Gently pull the threads forward above the needles to loosen them a little.
Pull the fabric back. The slack you created by loosening the needle threads should let it come out.
Flip the fabric over so that the underside is now up. Bring it around to the front so it looks like you are at the start of the seam.
Put the fabric under the presser foot and stitch over your seam for about 1 inch. Make sure your fabric is just a tiny bit to the left so that your seam stitches don't get cut by the knife.
After about 1 inch, stop and raise the needles. Loosen the threads again and pull your fabric out to the left.
Now that you're off the fabric, stitch a chain to finish.
This is how it will look. Trim off the chain and you're done!
It's not so tricky once you know how to do it, is it? I don't usually bother to secure the threads if I know that seam is going to get cut later by the knife when working another seam, but otherwise I do this on all my seams.