I use a stand-alone Babylock Coverstitch machine. You should be able to follow along with different brands, but some of the steps may be different (releasing tension, for example). Belinda has put together an excellent tutorial for ending the coverstitch on the Brother 2340CV, here.
1. Stop stitching with the needles in the highest position, or turn the handwheel to raise them if needed. Next, raise the presser foot and release needle tension. (On the Babylock, raising the presser foot releases tension at the same time.)
2. With a long, skinny tool (I use the needle allen wrench which came with my machine), sweep under the presser foot and behind the needles, "hooking" the needle threads.
3. Continue sweeping forward until the needle threads are pulled out in front of the presser foot.
4. Continue pulling the needle threads until you have a thread loop about 4" long.
5. Snip the thread loop in the center so both needle threads are cut at the same time. (I usually snip while the skinny tool is still pulling the threads out, but I couldn't balance the tool, the scissors and the camera all at the same time.)
6. After the needle threads are cut, pull the fabric straight back.
7. Continue pulling straight back until the needle threads are pulled to the underside (this will happen as you pull the fabric back), and stop when you have about 5-6 inches of needle thread.
(In this photo, you see the needle threads that were cut from the needles laying on top of the fabric. The needle threads in the stitches have just disappeared to the underside by my pulling the fabric.)
8. Turn the fabric over and there are your needle threads on the underside!
9. Cut the looper thread, leaving a 4-5 inch tail at the machine for your next project.
10. Needle and looper thread tails ready for next project.
11. Underside. These stitches will not pull out. Try it! You can finish the tails by threading them under the looper stitches with a wide-eyed blunt needle, tying a knot, or applying Fray Block.
(If you are hemming or stitching in the round, you will need to manually pull the needles threads at the beginning of your stitching to the back before you get to the end so you don't stitch over exposed thread tails. I usually stop hemming right before I get to the end to do that, and then I continue the last few inches, stitch over the existing stitches for 2-3 stitches and then use the method above to pull the ending needle threads to the back.)