Our toilet will out of the blue just start running for a few seconds and then quit. Any ideas on what I can try?

The flapper valve that flushes the toilet is leaking. Check to make sure there is slack in the chain (or other mechanism) connecting the valve to the flush handle. The rubber like material the valves are made of tends to deteriorate over time. Most require replacement occasionally, less expensive ones might require more frequent replacement.

Our toilet will out of the blue just start running for a few seconds and then quit. Any ideas on what I can try?
Two things will make a toilet run.
1) a faulty ballcock. If the water keeps running in the tank change out the ballcock **or**
2) a flapper that's bad or not adjusted and the water runs out of the tank. Let''s focus on the flapper because that's what it sounds like.
First let's check the flapper itself. Run your singer along the bottom of the flat edge. If it's wavy or ha rough spots then replace it. If it checks out good then
With the flapper seated the linkage wants to have 1/4" of play. Too much play and the flapper doesn't get pulled back enough giving you a short flush. Too tight and it lets water seep past the flapper. I adjust the chain by the link and if it needs fine tuning, I bend the flush lever rod a bit until I have the desired play in the linkage. One more thing about a flapper. you will see where the old flapper hooks onto the base of the white overflow tube. On a older type with no hooks the flapper has a ring that slips down over the overflow tube to the seat,(see image). If your tank has hooks, take a sharp knife or scissors and cut the neoprene ring off on the marks provided and hook the flapper on the hooks. Leaving the ring on will interfere with the flush. The water level in your tank should be 3/8 to 1/2" below the top of the overflow tube when the tank's filled. And the little tube wants to run from the ballcock and connect to the white overflow tube..