Mower just makes a loud clicking sound. Pulled the starter and it doesn't move at all. I am completely lost as to how to start this mower.

Usual Causes.
Low charge on battery
Bad starter/brushes
Bad selonoid
If you have a volt meter what's the charge on the battery and are all the cells good?

Im leaning to solonoid. That can be tested with a screw drive to jump the post. Follow this test check list..

If the battery is good, check the voltage to the starter by taking a volt meter and grounding the black probe to a good ground and touching the red probe to the starter terminal. Turn the key. If all 12 volts are going to the starter and the engine still will not crank, then starter must be repaired. If less than 12 volts are going to the starter, check for exposed areas in the wiring which could cause a partial ground or corrosion. Remove the corrosion, if any, and tape up the wire with electrical tape.

To check the starter solenoid after the starter was checked, remove the wire from spade terminal. With a screw driver, touch the spade terminal and the hot side of the solenoid. If the starter turns, the starter solenoid is good and there is a problem in the safety switches. The solenoid is usually located on the back side of the accessories panel, in the engine compartment, on Riders and Tractors. On Rear Engine Riders, the solenoid is located under the seat or in a seprate compartment. Follow the Positive (Red) battery cable to find the solenoid.

No Ground. Check the ground cable at the battery and where it connects to the engine or chassis of the power equipment. Replace if necessary cable if necessary.

Worn Brushes. Remove the starter and remove the end cap. Do this slowly as the brushes will fly out if you are not looking for them. If you have brushes from another starter, simply replace the brushes, or replace the end cap if brushes are not available. You must use brushes from the same starter as the one you are fixing. You can't use Tecumseh brushes in a Briggs starter or in a Kohler starter.

Hope this covers the problem here. If not get back please.