When you say finish - do you mean, make it stand out? My favorite way is to use trapunto to puff the pieces up higher. (I do my applique by hand).
So here goes:
An easy way to make your applique stand out is to use the trapunto method. If you've used cotton fabric, then all you need is some yarn and a sewing-up needle. Simply thread the yarn onto the needle (use dark color yarn with dark fabrics, light color yarn with light colored fabrics). Insert the needle on the back of the inside edge of the applique area, have it emerge directly opposite at the inside edge and smoothly draw the single strand of yarn through. You will not be knotting the yarn end and so may draw it completely into the applique area. Where the needle emerges, clip the yarn even to the fabric, push any excess back down into the applique area. Use your fingernail to smooth the fabric threads back into place, removing all traces of the needle holes. Repeat as necessary until your applique area is filled. Apply backing and batting after the trapunto is completed.