Push the start button and hold it in until the generator starts. The clicking is the fuel pump on the Generator.
Just hold the Button down until it starts.
If you push the button for OFF and hold it you should also hear the fuel pump running, this will prime the engine, then push the start button and hold it until the engine cranks. If you have the owners manual, read it and it will also explain the above. If you don't have the owners manual, search online for the specific manual based on the tag on your Onan.