I usually have a lot of trouble with applique but my mom taught me this little trick which I thought I would pass along. Note: this would not work if you were appliquing something where you would see the back side on the finished product.
First: Put a flattened coffee filter behind where you will be stitching and then change your stitch length so it is a tight zig zag.
Second: After you have carefully stitched around the piece you are appliquing you can tear off the coffee filter from the back. While doing this, it is important to put your finger on the back side of the stitches and press down so you do not tear out your stitches.
The finished product: Not perfect, but I'm working on it. I like using coffee filters because it provides some stability to your fabric and prevents your stitches from bunching and pulling funny.
Happy crafting everyone!