I really like to use the blanket stitch when I work with felt. It's a great stitch to join felt pieces together and looks very clean and pretty. For embroidery projects, it's very commonly used on edgings. The best thing about this is stitch is that it's very easy to learn!
Step 1 - Bring your thread out at A. Take your needle from B to C, keeping your thread under the needle.
Step 2 - Pull your thread until it looks like the pic above.
Step 3 - Take your needle from D to E while ensuring your thread remains under the needle like in Step 1. Pull thread through.
Step 4 - Continue Step 3 until needed and then finish by taking needle to the back of fabric after your last loop.