When trying to start I get only a click. Battery appears good, all other procedures required have been followed. What can be the problem, how do I fix, location of parts that need to be fixed or replaced.

Have you tried to jump start the mower? How did you check the battery ?
If all is good then it may be the solenoid switch, or the starter, starter is on the side of the engine, solenoid will be the first thing the positive cable from the battery goes to, there will be another wire going to the starter and one to the switch at least.

Be certain its not battery... had similar problem after the winter... I left battery in tractor in dec for a cold night I believe it froze... brought it inside and thawed it... put it on trickle charger... battery seemed good... put in tractor it had power... but when I turned ignition it just clicked... thought I had solenoid problem etc... had warranty so john deere looked at it and said battery was bad... said battery had charge but could not provide starting amps or something like that... new battery corrected problem... runs like a charm now.
Good luck