Usually, if you're handy at all.

Describe in more detail. Do you see any faint shimmers of water in the bowl (that would mean the water is getting past the flapper, so you would need a new one (very easy to replace). Just shot off the water to the toilet. Flush. Reach in and unclip it. Take to store to match it. (Alternatively, you can also describe to someone knowledgeable at the hardware store the toilet's age and brand of toilet and they'll steer you to the right one.)

Is the fill hose clipped to the edge of the overflow tube ? (It should be, and aimed into the tube.) It should not be just stuck down into the overflow tube.

Is the water level up to the edge of the overflow tube? Water needs to stop about 1" below the top edge. If it keeps running you need a fill valve (someone easy, but best to see it done once). I'd have a friend who's done it before show you how.

Good luck.

'Phantom flushing' is often noticed when the fill valve opens to top the tank off.

It is almost always caused by a bad flapper valve in the tank, or occasionally by a rough seat for the flapper valve in the tank.

Not a hard or expensive fix.

Try a replacement flapper valve first.

I just went through the same thing a few days ago.

First I cleaned the flapper seat and replaced the flapper, took a couple of minutes to do. Didn't solve the problem, so I bought an entire refill assembly from the box store, about $19 if I recall. New fill valve, overflow tube assembly, flapper and flapper seat.

Turned off the toilet supply, flushed, sponged the excess water out of the tank. Removed the three threaded bolts that held the tank to the bowl, then removed the tank from the toilet bowl.

Removed and replaced the fill assembly. Removed and replaced the flapper seat and flapper and overfill tube assembly.

Reinstalled the tank on the bowl.

Attached the flush chain to the flush arm, I had to tweak and bend the flush arm a little as the geometry was different from the old one.

Turn the water on, check for leaks, enjoy!

Took about a half-hour, I started during intermission of a Bruins hockey game and missed the first five minutes or so of the next period.

Not complicated, just take your time and don't overtighten any bolts. You want snug, but you don't want to crack the china.