Here is one technique in a 5-part series on how to finish seams.
French Seams Step-by-step Tutorial
Place fabric with WRONG sides together, RIGHT sides facing out. Stitch 1/4″ seam allowance.
Cut 1/8″ (or less) off of the seam allowance to get both fabric edges even and the seam allowance narrower.
Open the seam and press.
Turn the fabric to RIGHT sides touching and WRONG sides facing out. The seam allowance is sandwiched in between the layers. Press. Stitch 3/8″ away from the edge for a total of 5/8″ seam allowance (if that is the correct seam allowance for your project).
Press to one side. Voila!