Without a scan tool, You'd have to remove the negative side of the battery with the ignition switch on. This is called an idle re-learn as it'll reset your PCM completely in the process of clearing codes. As such, I recommend following the driving cycle for Idle re-learns that can be found at www.obdii.com for GM vehicles.
Otherwise, the PCM will clear them on it's own. Depending on the severity of the system failure, the PCM will clear the codes after either 3 CONSECUTIVE operating cycles without another failure or 40 CONSECUTIVE operating cycles.
For a failure like removing your gas cap, I believe it's the 3 cycles.