Chain stitch is a linear stitch.
Bring your needle up from the back of the fabric, and go to put your needle back down the same hole you've just come out of, bringing your needle back out a stitch distance away in one movement. Loop your original thread under the needle before you pull the needle through.
Repeat this, using the new point your needle has come out from as the starting point. Keep working this along your line. When you reach the end, make your final stitch to take your needle back to the reverse of the fabric, anchoring the final loop of your chain in place. Fasten your thread off.
Couching is used to fix braids, ribbons or trims which are too thick to go directly through the needle.
Place your trim on the fabric (if possible you may find it helpful to pin it in place) and then work a series of stitches bringing you needle up below the trim, and putting it back through the fabric above the trim so the trim is caught underneath the stitches.
If your trim is likely to fray (for example, most ribbons), cut it longer than you need, and fold a little section underneath at either end so there are no exposed edges. If your trim won't fray, it's easier to cut slightly longer than needed and trim off the excess once you've stitched it down.