Feathered Chain Stitch is made up of long tailed chain stitch worked in a zig zag manner. Long tail chain is simply a chain stitch with a long tie stitch. If you are beginner you need to be able to work chain stitch before doing this variety.
Each long tail chain stitch is worked on a diagonal slant, alternating from left and right. I find it easier to work this stitch from top to bottom between two imaginary lines bit if you want neat zigzag line some people find it useful to mark the fabric with two parallel guide-lines.
How to work Long Tail Chain stitch
Bring the needle up through the fabric on the right hand line. Insert the needle back into where it emerged from and take it through the fabric bringing the point of the needle diagonally across the line as illustrated. The needle should point towards the left.
Wrap under the needle point as you would for chain stitch and pull the needle through. On the same diagonal line tie the chain down with a long straight stitch. The tie stitch should finish on the left hand line.
When this stitch is worked in a single unit it is called a long tailed chain. I think readers can see why. You can arrange long tailed chain stitch is all sorts of ways. Circles are a common pattern as they then look like flower petals. There are also varieties that weave the spokes created by long tail chain when arranged in a circle.
You can find some of these varieties illustrated here
How to work Feathered Chain stitch
To make the second stitch bring the needle up through the fabric on the left hand imaginary line, close to the end of the tie stitch. Have a thread or two between where the tie stitch went into the fabric and where your needle emerges.
Work another long tail chain stitch pointing back towards the right hand imaginary line.
Continue in this zig-zag motion downwards.
This is not a true feather stitch as such but that is what it is referred to in books. I think of it as zig zag chain stitch. Hope you enjoy this stitch.