Ron, there are a few things that will cause an otherwise healthy engine to shut down. Lack of spark, fuel/air mixture is wrong, or excessive load (binding belt, pulley etc.) overloads the engine.
The coil that supplies the power for the spark plug on that engine is pretty reliable. At this age, the wire may be cracked or broken in places, so inspect and replace if needed. I'd also put in a fresh spark plug at the same time.
The H2113 has a number of safety interlock switches that can shut down the engine. If any one of these is flaky, or has a poor connection, the spark to the engine will be shut down:
Brake pedal switch
PTO lever switch
Seat switch
Neutral switch (on transmission)
There is also the interlock relay and ignition switch as well, and either of these can possibly cause the engine to shut down if they are not making proper contacts. Same goes for any location on the wiring harness. The switches for the Seat, Parking Brake Lever, PTO lever, and Neutral are all normally open (no connection). They are closed (connected) when the tractor is ready to run. The interlock relay must get a ground through the Seat Switch OR the PTO switch, Neutral switch, AND Parking Brake Lever switch.
That said, electrical stuff is usually pretty durable, and it either works or it doesn't. You just have to try and find the fault when the tractor is in a "no start" condition.
Now the fuel/air side can be a possible problem area too. Often, debris or gunk inside the carburetor can form when the fuel is left too long in the tractor. A good cleaning of the carburetor and flush of the fuel system is probably a good idea given the age of this tractor. Sometimes, it's faster and easier to just replace a carburetor, rather than trying to overhaul one, especially if you've never done it before. A new carb for this tractor has a list price of $80.65, and is available from any Honda dealer; use Part Number 16100-AF5-V02.
When the tractor fails to start, does it turn over with the electric starter okay, but just doesn't start? This would indicate there's not a jammed belt or other heavy load. You can pull the spark plug, reconnect it to the cap, ground the electrode to the engine block, and then turn the key. You should see a faint spark jump across the electrode. If not, it's likely an electrical issue. If you do get spark, probably something the the fuel system (carburetor is often the main thing).
For DIY, I'd suggest at least getting a paper shop manual. Honda sells them direct on eBay, with free updates for 3 years. Here's a link:
Honda Shop Manuals on eBay
Hope this helps you get "started."