Turn off the water supply to the leaking pipe.
Dampen a rag with isopropyl alcohol and clean down the leaking section of copper pipe to remove grease and oil.
Rub down the leaking section of the pipe with a 300-grit sandpaper until the copper surface is rough to the touch. This will ensure that the epoxy bonds to the copper.
Mix the epoxy and epoxy hardener included in an epoxy kit in an equal 1:1 ratio for 60 seconds. Use a clean plastic bucket for the mix. The instructions for some epoxy kits vary by manufacturer. Be sure to follow the directions closely as indicated on the epoxy's package.
Scoop the epoxy out of the bucket and spread it onto the copper pipe. Use a putty knife to spread and manipulate the epoxy. The epoxy will cure in 30 minutes after application. Turn on the water to the pipe after 60 minutes.