To replace a handle for a Spring Faucet, locate the small, round set screw cover on the handle.

Pop the cover off by getting underneath it with something thin like a utility knife (providing you do not want to keep the handle for any reason. If so, be careful not to damage the finish). 

Once the cover is off, use an allen wrench to remove the set screw inside.

Pull the handle straight out to remove the handle and expose the top of the cartridge.

Repeat this process for installing the new handle.