The easiest way I know of is the "starch method" of preparing the edges of the petals.
This site explains the whole process - if you're only doing the petals on the Dresden and perhaps the center circles, it will be much simpler than the process as shown.
After turning the edges under, you can then use Elmer's Washable School Glue or Roxanne's Glue Baste-It and glue the raw edge of the turned-under part and press the plate onto the squares of backing fabric with a steam iron.
The glue holds the fabric in place without interfering with getting the plates sewn onto the backing squares. But, it washes right out - soak the block in warm water and then give it a scrub between your thumbs. The glue comes right out. :)