I have a Craftsman mower. I was mowing when it suddenly ran very high, then slowed way down and stopped. I started it and it ran for less than a minute but very slowly again. I thought it was out of gas so I filled it and now it won't start at all. It usually starts on the first pull. I tried putting a little fuel where the spark plug goes, as I've seen some suggest, but that didn't start it either. Any help appreciated before I have to haul it to the repair shop.

First and foremost, do you have fresh fuel? Your sequence of events implies that you started with the old fuel. Did you treat that remaining fuel in the tank over winter?
Likewise with fuel that was stored over winter.

Yes, the fuel is fresh. I had just mowed the front yard the day before. I live in San Diego, so it it used most of the year.

Here's a basic video on troubleshooting:
Lawn Mower Repair : Troubleshooting a Lawn Mower - YouTube

Also, how's the air filter?
Diaphragm between tank and carb torn or distorted?
You can also search for youtube videos on correct operation of governor.

I will, thank you.

Good luck. Another remote possibility is the plug wire especially if it is an older mower.
Carefully, try starting it in the dark and look for arcing, if all else fails.
That "running high" you described could indicate a governor malfunction.