Remove the awning from the RV. Some of the work you will be doing is delicate, and it will be difficult to do if the awning is still attached to the RV. Unroll the awning in a clean, dry area, so you can work on it.
Prepare the awning. If the edges of the hole you are repairing are ragged, you should cut them into a regular shape. If the hole is due to mildew, you should likewise remove the most effective areas. This may seem counter intuitive, as you are making the hole larger, but the fix will hold better. Finally, using a bleach solution of 20 parts water to one part bleach, gently clean the area around the hole on both sides of the awning to remove dirt, lint, and mildew. Let the awning dry thoroughly before proceeding. You can accelerate this with a fan or space heater.
Prepare the patch. Many RV users tend to cover smaller awning holes with waterproof tape, but this is only a temporary fix and not recommended. Patching material can be bought directly from your RV's manufacturer, and this is recommended to keep your awning looking uniform. Cut a patch to cover the hole with at least an inch of overlap on each side. Bigger is better than too small.
Paint the edges of your patch with adhesive. Place it over the hole on the outside of the awning. Then, apply adhesive to the edges of the underside of the patch from the other wide of the awning. This will complete the waterproof seal of the patch. Again, let this completely dry before taking any further steps.
Reattach the awning to your RV after the patch has dried. You can now roll the awning back up and use it normally again.