How can I replace carburetor?

"runs great" is subjective. Likely all it needs is a valve lash adjustment.

Kohler SV710 0.005in. +-.001

Drain carburetor bowl and try again. The engine will not run if the bowl is full of water. If it works try and figure out where the water came from (check fuel containers).

Check the anti-afterfire solenoid is functioning. This is the solenoid at the bottom (or side) of the fuel bowl.

It is safe to use starting fluid sparingly. A simple short <1 second burst into the carburetor throat is all that is needed. Where people get into trouble is they spray a few seconds and saturate intake with fluid and it pools inside a cylinder.

Jason, You can replace carburetor or have the old carburetor rebuilt to fix your gas leaking problem, either float is stuck or if carburetor equipped with a solenoid shut off, are the actual problem likely.
Check the attached links,instruction and guides, Good luck
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Carburetor Rebuild Cleaning Instruction Video
3 50cc Scooter Moped Carb Theory and Common Carb Problems
How to clean scooter carburetor
rebuild scooter carburetor Google Search

Sounds like an air filter, choke or carburetor problem. rebuild kits are available for most small-engine carbs, but first try replacing the air filter and cleaning the carburetor and choke with spray carb cleaner. Instructions are available at:
http://www.briggsandstratton.com/us/en/support/faqs/adjusting-the-carburetor
http://www.youtube.com/watch?v=VBL-BUj0c6E
and elsewhere.

That is a fuel shut-off solenoid. It is an anti backfire device. You can test it. Remove it from the carb assembly, plug the plug into it ( if only one wire to plug then it needs to be grounded- hold it against part of the crankcase), turn the key on with the brake locked. You should see the pin on the solenoid suck in. Turn the key off and the pin comes back out. Repeat several times and make sure it doesn't stick. If the pin doesn't move then you need you either have an electrical problem or the solenoid has failed. Be sure fuel is flowing good to carb first, then be sure carb is clean, then suspect shut-off solenoid ( they are 70-100 bucks to replace)

It is a fuel shut-off solenoid. Its purpose is an anti backfire device. Its likely the carb is just dirty as opposed to the solenoid failing. But if it has failed it is about $70-$100 to replace. Test the solenoid by removing it from the float bowl and plugging the wire back into it and holding/ grounding it against the crankcase, lock the brake, and turn the ignition key on. You should see the plunger of the solenoid suck in with key on and release with key off. If the solenoid works properly clean/ rebuild the carb. If not working properly clean/ rebuild the carb ( the same stuff that caused the solenoid to fail is still in the carb) and replace the solenoid.

Make sure that the gas Is not tighten all away down. Often times it causes a vacuum to form in the gas won't feed out of the tank properly. Loosen the About a quarter turn and see if that works.

A new carburetor will definately help. The old carburetor may have some ports still clogged. I would also spray some penetrating oil in the spark plug hole to help loosen up the rings on the piston. It may smoke alittle when you fist start it up. Plus try some "engine start" spray, to see if the engine will crank.

If this tractor/engine has a fuel solenoid at the bottom of the carburetor, with a small plastic plug in on the side of it, you will have to unscrew the solenoid to remove the bowl. It takes a very thin 1/2" wrench to reach the flat sides on the solenoid and not mess anything up. I use an old tappet wrench but I don't know if they even make those anymore. If you have to, get an old cheepie wrench and grind it down equally on both sides where it will fit. If it doesn't have the solenoid you should be able to just remove the bowl nut and gently tap the lower edge of the bowl to break it loose.
If the thing is badly varnished up, you should remove it completely and rebuild it or replace it. There will most likely be varnish in the main jet as well as just the bowl and sometimes replacing is the better alternative.
If you want to post the Sears Model number, I will look it up and tell you the difference in price of kit vs new.

Most of the starts but dies problems are caused by dirt/water/debris in the carburetor float bowl.

You can try draining the gas out of the carburetor float bowl by removing the float bowl nut located on the bottom of the carburetor.

Make sure the hole in the float bowl nut are clean. If the problem persists after draining the float bowl nut you will have to remove, dis-assemble and clean the carb with compressed air and carb cleaner.