Can't quite see, but probably the yellow plastic has inside it the ballcock valve that is supposed to shut off the water intake when the tank has filled back up to its usual level after flushing, and the ballcock valve is beginning to fail. It's the most common problem with toilets.
See if you can find the pipe that brings water into the toilet tank. With a bit of luck, it will have an inline valve on it that you will be able to see, before it goes into the tank. It will either have a lever or a screw head that you can turn to shut off the water intake into the tank. If it does, you can very easily shut off the water going into the toilet. It's probably then just a matter of unscrewing the yellow plastic part that looks as though it has the ballcock valve inside and replacing it.
If you can't find an inline valve specifically for that toilet you will need to trace the pipe bringing water into the toilet tank back to the next point at which you can shut off the flow of water. Flush the toilet until there is no more water coming through (in case gravity is going to push out the water left in the pipes) and again replace the ballcock valve.
The next most common fault with toilets is a failure of the syphon that allows water to flush the toilet. The process of replacing a syphon is pretty much the same.
