How can above ground pool be repaired

It sounds like the hole is relatively small. You can make a patch using a piece of sheet metal or a piece of flat aluminum which you can purchase at Lowes or Home Depot in the hardware dept. Use sheet metal if the metal surround is metal. Use aluminum if the surround is aluminum. You can tell which is which by taking a magnet and touching the metal. If the magnet sticks, it's metal not aluminum. Cut the patch using sheet metal shears to a size that is 4 inches by four inches larger than the hole. Then you'll have two inches on each side of the hole. You are going to need to put the patch on the inside of the metal, between the liner and the metal surround. This so the hole edges won't tear the liner. When you cut the patch, round off the edges so there are no sharp edges. Take duct tape and cover the edges of the patch. Place 1/2 the width of the duct tape and apply it to one side of the patch and fold the other half over to the other side. You can cut a round patch, but a square or rectangle patch will be easier. Just cut the corners round. Purchase a small tube of silicone sealant ( when you but the patch material) and apply a bead around the patch edges and in the middle. Then affix the patch over the hole. Wipe off any sealant that ozzed through the patch so it doesn't bond to the liner.