Are you sewing by hand or with a machine?
I do both and there are hints for both!
THE biggest think I can think of for machine applique: Use a second layer of fabric to act as a stabilizer. I cut a piece of scrap fabric and spray it with 505 spray and attach it to the back of the design area. When the design is completely appliqued you can pull the fabric back and trim close to the stitching. There's no puckering at all that way!