DIAGNOSIS The starter solenoid is clicking but the starter motor isn't engaging. This is almost always a poor connection at the battery terminals.
FIX Disconnect the negative battery cable first. Remove both battery cables completely. Clean the battery posts and the inside of the cable terminals with a wire brush until shiny metal shows. Reconnect, positive cable first, then negative. Torque them firmly.
IF THAT DIDN'T WORK The starter motor itself could be bad. You can test it by jumping 12V directly from the battery positive to the starter's terminal (with the generator off). If it still doesn't crank, the starter needs replacement.
HEADS UP Never work on battery connections with the generator running. A loose battery connection can also cause erratic voltage output from the generator while it's running.