I like to use lightweight interfacing or muslin to applique. Take the applique piece and put it right side together with the interfacing and sew . I usually leave the interfacing in a shape bigger than the applique piece. After I sew them together. I trim and cut a slit in the back and turn to the right side and press. Your edges are turned under. I stitch them on my machine using the blanket stitch or zig zag. You can use a glue stick to put them down before you stitch to keep in place.
If you have tiny pieces to applique this would be a little tedious.
Google Eleanor Burns (quilt in a day) she has the same technique and you could see how it's done.