Bias binding is a great way to finish raw edges on garments. It's a good alternative to using a standard facing, particularly if you are short on fabric.
I used 12mm single fold binding to complete the steps below. I've also used contrasting thread and binding to make the photographs clearer, but using coordinating thread and binding would make it look more inconspicuous.
1. Take the binding out of the packet and unfold one edge of the binding. Alternatively you might prefer to make your own binding.
2. Fold the very beginning of the binding over approximately 5mm and pin to the garment.
3. Using the crease of the fold in the binding as a guide, pin to the edge of the garment, matching up raw edges.
4. Pin all the way around the garment until you are back at the beginning (where you folded over the edge of the binding). Make sure that the end of the binding extends over the original fold. The image shows how it will look when it is sewn (the next step!). Pin in place for now.
5. Sew this to the garment, using the pins and crease in the binding as a guide. Make sure you keep your seam allowance accurate.
6. Then use small scissors to clip in to the seam allowance. Be careful not to snip through the stitching line.
7. Press the binding away from the garment.
8. Pull the binding away from the garment, and understitch onto the binding. Make sure you catch the seam allowance underneath. You need this stitching line to be close to the actual garment without actually stitching on the main garment.
9. Fold the binding to the inside of the garment and press. Pin the loose side of the binding down.
This picture shows the join in the binding when finished from the wrong side.
10. Sew the binding down by sewing around the opposite edge of the binding. I like to sew this from the wrong side of the garment.
And here it is from the right side of the garment. It would look better if the binding and thread was also white, but it's easier to show the steps with contrasting binding and thread.