There are a couple of different methods that you can use.
You can use a single layer of fabric. This method is best used with a more traditional pocket shape which has a straight edge along the top. First turn the raw edge under toward the wrong side of the fabric around the bottom part of the pocket and press it with an iron. Use a narrow allowance such as 1/4 inch. If there are curves you may need to press some of the fullness into the seam allowance. Just press the creases as best you can to achieve the shape that you want and get it as flat as possible.
Next, fold down the top edge a narrow seam allowance. Then fold it down again so that the raw edge is enclosed in the folds. You are essentially creating a hem. Stitch across this to encase the raw edge.
After hemming the top edge of the pocket, you can place it on your garment and sew it into place around the bottom edge using a very narrow seam allowance. The seam allowance should only be about 1/8 of an inch.
Cut out 2 identical pieces for each pocket.
Place them right sides together and stitch them together using a quarter to 3/8 inch seam allowance. Leave a small opening for turning.
Trim seams if needed and notch curves if needed. Turn right side out. Use a chopstick or other similar implement to poke out any corners until they are nice and square. Press with an iron. Make sure that the little bit of raw edge from your turning opening gets pressed up between the layers of fabric. Topstitch across the top edge of the pocket to give it more stability.
Place your pocket on your garment piece and stitch into place making sure to secure the raw edge from your turning opening. Stitch approximately 1/8 inch from the edge of the pocket.
There you have it. Two simple ways to add patch pockets to your garments. You can dress them up by adding embroidery, lace, rickrack, piping or coming up with your own idea!