If the foam is damaged within your cover sadly there is not a cheap or easy fix. However if the vinyl is damaged the fix is easy and cheap.
To repair your vinyl cover you must first find some waterproof glue at your local pool store. This glue is commonly used for patching vinyl pools. The glue costs between $10 — $15. You will also need material that is the same grade and color preferably as your current cover. Most of the vinyl covers are made from marine grade vinyl and your local pool store should be able to help you out with finding this material. If your local pool store does not help another option is an upholster. Buy enough material to cover the damaged area and leave a little extra just to be safe. For instance if you have a 2 cm x 2 cm damaged area you should buy no smaller than 3 cm X3 centimeters.
Once all materials are at hand cut the corners are round to ensure that if the patch comes loose the corners will not curl. Apply glue to the bottom of the patch and flatten it out on the damaged area and let dry for at least 24 hours.