This shows how to finish an edge of a non-fraying fabric with a lining of fraying fabric, in this case wool fabric and cotton lining, with a blanket stitch.
The same method can be used if there is only a non-fraying fabric, but then it is not necessary to fold the edge. It can also be used with fraying fabric, but then the fabric should be folded over twice so the raw edge is covered.
Start with tying a knot to the end of your thread. Pull the needle and thread through the wrong/lining side of the fabric, right below where you want the edge of the folded fabric to be.
Put the needle down in the exact same point as you first did. Pull the needle through, but do not pull the thread completely through.
Fold the fabric over. Make sure the raw edge of the lining is covered by the main fabric.
Pull the needle through the loop that is going over folded fabric. Pull the needle in the same direction as you want the stitching to go. In this case I wanted it to go to the right, so I pulled the needle through from left to right. Pull the thread tight.
Pull the needle and thread through the fabric right above the folded edge, but do not pull the thread completely through. How far from the first stitch you should put this depends on how close you want the stitches to be. I used about 1 cm between mine.
Pull the needle through the loop and tighten the thread.
When the thread has been tightened it should look something like this. You now continue in the same manner. Pull the needle through right above the folded edge, then through the loop the thread makes and tighten.
When you want to finish and fasten the thread, tie a knot with the thread at the wrong side of the fabric. Try to place it close to the point where you last pulled the needle through.