It depends on if the copper pipe is threaded or not. If it is (I'm assuming you're replacing the faucet), you will replace the old faucet with a new one in the same way you would with any other kind of pipe.
If it isn't threaded, and the leak is where the pipe joins the faucet, you'd have to cut off the end that inserts into the faucet, and use either solder or a compression fitting to put a new end on.
Here's how to solder it on:
If you use a compression fitting, watch out that you don't tighten it too much:
If you're connecting copper pipes to plastic, you'll want to insert a liner in the plastic pipe to keep it strong and not leak under the compression fitting: