Once you have made your detached chain stitch, make another detached chain stitch on the outside of it. To do this, ring your needle up a little above where you came up to start the first stitch. Take it down again right next to that spot and bring the point up at the end of the catch stitch from the basic stitch. Make sure your thread is under your needle point before pulling the needle through to create the loop which should lay around the outside of the first stitch.
Make a catch stitch (a small straight stitch that "catches" the loop thread and secures it) on the outside or second detached chain stitch.
Here is the series of completed Double Detached Chain Stitches I made. Looking at it now, I wish I had used threads with more colour contrast to make it easier for you to see. I hope you can make it out though. Basically each Double Detached Chain Stitch is a single Detached Chain Stitch and then a larger one which goes around the outside of it. In my example the inner stitch is light blue and the outer stitch is purple. If you need a better example I can work one up in perle cotton - just let me know!