Why Does My Water In Toilet Keep Running?

The flush valve is not closing. If the tank has a flapper, rubber valve, the culprit is usually the chain connected to the flush arm. Free the chain so that the flapper drops into place. Check that the flapper is properly aligned with the flush valve opening. Replace the flapper if it is decayed or distorted.

This sounds like a a flush valve sticking you can get a flush kit at most department stores Walmart or construction supply houses like Home Depot or Lowe's it is really not hard to install yourself, the directions are usually included

This could be one of many things. 1) the float is set to high and water is going into the tube that goes to the bowl. 2) the flapper seal is worn out and needs to be replaced. 3) the water valve is stuck and needs to be replaced. 4) there is a crack in the tube or flapper seat.

Try lifting up on the float to see if it stops. If so, adjust the float by bending the rod so the float is lower in the water. If not, flush and let the water out of the tank. Reach down and feal the edges of the flapper to make sure it feels like a good piece of rubber and there are no tears in it. The valve is usually needed if you lift up on the float and the water does not stop coming in meaning it wont shut off. The last thing I mentioned means replacing the toilet or at least I have never heard of it being able to be replaced.

A device inside flush is faulty. There is a simple device inside the flush which needs repair or possibly should be changed. If you don't have any previous experience then you have to take the services of a plumber.

You have a close coupled toilet with a built in overflow the cistern is filling up to much so the overflow runs down into the pan you need to adjust ballcock in cistern

Sounds like the float is out of adjustment check the chain that goes from the handle to the flap also