When you know you'll be washing an item you sew, you'll want to make sure that the seams are finished to prevent fraying. There's lots of ways to do this, but in this instructable I'll show you how to finish your work with a flat felled seam.
This can be done on curved seams, but it's easiest on straight ones. I'm using two squares of fabric for this demo. I'll stitch with white thread so that it's a little easier to see, but you should use whatever thread best matches your project. I've sewn this using the machines at TechShop.
To begin, prewash and iron your fabric. Yes, it's a boring chore, but do it anyways.
Step 1: Right Sides Together, Sew
Place your pieces together with the right sides facing in. Make sure the edges you'll be sewing are aligned properly, and pin if necessary. Sew your seam 1/2" from the edge (or sew whatever seam allowance your pattern tells you).
Step 2: Press and Trim
Press your seam open. Trim 3/8" off of JUST ONE of your seam allowances, leaving 1/8" behind. Don't trim the other side.
Step 3: Fold, Press, Fold, Sew
Fold your remaining seam allowance over itself by 1/4" and press (see photo if you're confused). Then fold the whole seam allowance over to cover the part you trimmed. Finally, topstitch a scant 1/16th in from the edge of the folded seam allowance.
Step 4: Ta-Da!
You've done it! Your seam is finished nicely on both sides of the fabric. All of the raw edges are encased inside your flat felled seam. This seam is durable and stands up to washing well. Have fun sewing!