You need to locate the larger screw that has a jam nut. This is where the starter’s nose goes into the clutch housing. You need to loosen the jam nut, then back the tapered screw out. The rest of the starter will fall out. When loosening the set screw, you might want to hang onto the starter.
Most likely your battery is in good condition, your problem may be the battery connections. This would be where the ground cable attaches to the tractor frame.
If the battery connection is clean and the cables are in good shape and doesn’t start, I’d try to take the starter’s button cover off. There should be 2 screws holding it on when you remove the starter rod. You also want to check the contact surfaces.
Over time, these cables and connections can become slightly burned. Then you can clean up the contact on the starter button cover with the *** of a flat file. Scrape across it and brighten it up.
The starter case has a lug that can be touched up. You can use a chain saw file to clean this. If the starter button is bad, it needs to be replaced. If you have a NAPA, take it with you, in order to match it up. The lug in the starter case can be replaced if it’s burned badly. It’s normal to have a rounded cove in that lug.
If the original battery cables need to be replaced with automotive cables, such as 4 gauge, the cables need to be 1/0 copper cables, similar to the originals. I’m assuming you have the 6V system.