Carefully inspect the damage and determine its nature. The hole may have a smooth or jagged edges. This depends largely on the method of its correction.
If the cut is smooth, take a small piece in the fabric color of the coat and smear it with rubber glue "BF-6". You can also use the "super moment", "Moment Crystal" or "Aquasure". Then gently push the rag inside the hole, align the edges and secure. After a while the glue will harden and damage is resolved.
Handle smooth the edges of the hole can also be a decorative seam, for example, in the form of a zigzag. It is better to take thread in the color stick, or different by several shades. Contrasting stitch also will look good if the jacket has small parts and features of similar color.
Fix a hole in a down jacket with jagged edges, a bit more complicated. A good method is to applique brand label or tag. They should be careful to sew on top of the damage.
In specialized shops you can buy the transfers and using them to patch the hole in the jacket. To do this, place the damaged area of fabric on a flat surface and place it on the sticker. Well then iron with a hot iron across the paper or thin fabric.
If the damage is very large, the edges are rough, and the surface came down, must overhaul. The first step is to get rid of excess fluff. Take Scotch tape and glue them to the edges of the inside holes. Then the sticky side of another line of tape collect the feather. Now, cut two large pieces of fabric, identical to that of the jacket. First spread one rubber glue, place the inner side of the damage and press the edges of the hole. Wait until dry, and glue the other piece on the outside. That patch was beautiful, you can cut it in the form of some figures.