To fix a copper pipe leak at the joint, you can follow these steps:

1. Turn off the water.
2. Locate the nut at the central portion of the joint.
3. Look for solder.
4. Check the alignment.
5. Heat the reset joint.
6. Connect the two halves.

Alternatively, you can clean the damaged area with an abrasives pad and then add flux to the pipe. Heat the flux with a blowtorch until it changes color and then add solder into the hole. This will block up the hole, sealing the leak and returning the pipe to full working order.