Here is one technique in a 5-part series on how to finish seams.
Hong Kong Seams Step-by-step Tutorial
Place fabrics RIGHT sides together. Stitch with the seam allowance called for in your pattern. The example is 5/8 in.
Press the seam open.
Align the raw edge of a bias strip with the raw edge of one side of the seam allowance.
Stitch the bias strip and seam allowance together with 1/4″ seam allowance.
Fold the bias strip back over and press.
Fold the bias strip to the back side of the seam allowance.
Stitch the folded bias strip in place.
Trim any of the excess bias strip from the back side.
The seam is finished after being trimmed.
You can stitch either on the bias strip or directly next to it, which is called stitching in the ditch. I prefer the stitching in the ditch method, I think it makes a softer seam.