My husband lost the keys to our truck, so we got a new key made at a locksmith. We were told by a friend that it's possible to program the key ourselves, but does anyone know how? It's a 2003 Chevy Silverado truck.

Are you talking about programming the chip inside the key so that the truck will run or are you talking about a remote key fob?

If you need the chip in the key programmed, you have to have it done at a dealer. If it's the remote key fob that you're talking about, you can do it this way:
Chevy Silverado Keyless Entry Remote Programming

This video may help byut you have to watch the coomercial first, only can be done if you have one key left. If you have no keyes at all you can't do it yourself. How to program a transponder key GM Chevy Buick Saturn Oldsmobile Pontiac Van - YouTube

Have you tried the key and found that is didn't start the engine?