When I try to start my sears lawn tractor Model 917.2171080 it clicks the fuse is good, the battery is new how do I trouble shoot between starter and solenoid.

Hi,
I would say you have a bad solenoid, it clicks but does not make an electical connection.
Peace,
Clarke

Hello.
Make sure you have a fully charged battery. Needs to be reading in the 12.7 to 12.9 volts to turn the engine over. Is the clicking just coming from the solonoid, If so check for voltage at the positive lead on the starter. If you have voltage at the starter when you engage the key, the starter may be bad and proves the solonoid is working. Try jump starting the mower by using jumper cables attached to the positive post on the starter and negative to a good engine ground. If the starter engages and the motor turns over, your starter is good.
Good Luck.
Dave

Before you go too far you might want to try to turn the engine over by hand. Sometimes the starter will get stuck engaged. Simply turning the engine by twisting the top of the engine will let it pop loose. Then see if it will crank with the key.

More than likely it will either be the solenoid, starter or a battery cable.