Step 1: What you need
-one package satin blanket binding (at least 140 inches long, I use Wrights)
-a sewing machine and knowledge of how to use it
-something to mark your fabric like tailors chalk
Step 2: Wash your fabric
Step 3: Measure your fabric
Once you have your marks, pin the pieces together near the marks so that your fabric doesn't slip when you are sewing.
Some people put little yarn ties through both layers at measured intervals or use another quilting technique so that the fabric doesn't slip against itself when it is a blanket. If you want this, then now is the time. In my experience, these blankets are small enough and flannel sticks to itself well enough that you don't really need it for practical reasons.
Step 4: Sew the fabric together and cut
Step 5: Zig-zag or serge the raw edges
Technically you don't need this step, but I like my blankets to be as sturdy as possible. It also helps stabilize the edges, which makes it easier to apply the binding.
Step 6: Prepare binding
Then prepare the beginning of the satin. With the folded side away from you and the shorter side up, the beginning end is the one on your left. Take this end, open it up. If the edge isn't even, cut it and gently burn the edges with a flame to keep them from fraying. If you burn too much you will scorch it and it will become all wrinkled. Re-cut and start over if this happens. Then fold the ends to the middle fold so you are left with a point -- like the first steps of making a paper airplane. Close the satin and adjust so that the folds line up on top of each other. Iron.
Step 7: Attach the binding: initial and straight edge
I will refer to two zig-zag stitches:
-zz1 is a very tight (short stitch-length) zig-zag such that the zigs barely clear each other. You want the width to be ~3/16 inch. On my Brother machine the stitch length is 1.0 and the stitch width is 5.0.
-zz2 has the same width but a longer stitch length (~1/8 inch between zigs), something that looks pleasing to you. On my Brother machine the stitch length is 2.5 and the stitch width is 5.0.
When you sew the satin on to the blanket, stitch near the edge of the satin. Because the shorter side of the satin is up, you will always catch the longer edge, but you want the zig-zag to straddle the satin edge on both the top and the bottom.
Sandwich the flannel in the satin at the prepared end so that the shorter side of the binding is up and the fold of the satin lines up with the blanket edge. Do this so that the satin covers a little more than half of one of the blanket sides. Pin from the beginning of the satin to the corner of the blanket. Starting at the tip of the folded satin, use zz1(backwards then forwards) to secure. Make sure you are catching both the top and the bottom edges of the satin! Then use zz2 to continue stitching to the end of the blanket. If the satin slips some and you have to adjust the pins, don't worry, that is why we are only doing one side of the blanket at a time. Your flannel might have a little fold right at the end near the straight stitch, and that is OK too because it will be covered by the satin and no one will know! When you get to the end, back-stitch about 3 or 4 stitches to secure. Cut thread.
Step 8: Attach the binding: mitered corner
Pinch the edge of the blanket and open up the satin. Bend the satin so that the corner of the satin and the corner of the blanket are at the same place, then close the satin so that there are satin folds coming out at 45 degree angles from the corner. Pin.
Now sandwich the rest of the blanket edge between the satin and pin to secure.
Since the satin is slippery, the folding can get a little funky. I usually pin the back of the blanket then the front. Then put pins all the way through and remove the first ones. The trick is to get the 45 degree folds to line up on top of each other. When you sew, you want the zig-zag to straddle the two edges, so the folds you have to be symmetric to within your stitch width.
Now that you have your folds pinned, use zz1 to secure the folds near the corner (back and forth about 4 stitches each), then switch to zz2 to finish the 45 degree folds, turn the corner, and sew the rest of the blanket side. Again, adjust the pins if needed, just make sure that the middle satin fold lines up with the flannel edge.
Repeat this twice more. For the last corner, pin, but don't sew yet.
Step 9: Finishing
Finish pinning the satin around the blanket edge taking care to make sure that the tip of the satin is even with the edge of the blanket. Sew the corner as in the previous step and use zz2 on most of the rest of this side. Just before the tip of the satin, use zz1 (back and forth) to secure.