I have a Riding mower Sears Model 917275660 with a Kohler Engine Model Number SV600, Type number 0001. The engine will not start. I have a new Battery but when I try to start the only thing I hear is the Solenid on the botton of the caburetor clicking. How can I correct this?

So the engine wont turn over at all? Well, we know the fuse is good since the fuel solonoid is getting power. Do you have a test light? Locate the starter solonoid, check for power to the small spade on the starter solonoid when the key is turned to the start position. Be sure the brake pedal is depressed, the pto is disengaged, and that the seat switch is depressed.
If you have power to the small spade then check the large posts for power. The battery side should have power all the time and the starter side should have power when key is turned to start. If you have power from battery and power from key switch but no power to starter then the starter solonoid is suspect.
If solonoid tests good and power is getting to starter but starter doesnt engage then starter is suspect.
If no power to small spade on starter solonoid then you will have to do some back tracking. It could be the key switch, one or more of 3 safety switches or bad wire/ bad connections