Simply stated, applique involves cutting a shape out of one fabric and sewing that shape onto another fabric. If you ask any quilter or sewing enthusiast, they will tell you that all the different methods used to add applique designs to garments and other fabric items can fill a book by themselves. However, I will explain just the basics which are easy enough for anyone to do, and they can also be modified and adjusted to suit the tastes of even the most advanced crafters.
The first thing you usually need for appliqueing is a pattern. This can be from a purchased pattern, coloring book page, or even a hand drawn design. It is easiest to transfer each aspect of your pattern separately onto paper-backed, fusible webbing by tracing it; however, be aware that your pattern will be reversed once it is ironed onto your fabric so everything should be drawn and written backwards! The traced pieces can then be ironed onto the back side of the fabric. Once the paper cools, you can cut out the design, remove the paper backing, and iron the design fabric onto your fabric item.
If your fabric item will be heavily used and/or frequently washed, such as an article of clothing or a table cloth, secure the edges of your applique using a tight zigzag stitch on a sewing machine or by tracing the outline with dimensional fabric paint. If the item will not be washed or used as often, you can leave it as-is or you can hand sew fancy stitches around the edges.