Not are what the problem is. Brand is Koehler 1.6 gal per flush
Water running but not filling or no water staying in tank?
Running but not filling
your flapper isn't sealing.
tjdabomb is probably right. This means:
1) you need to check to see if there is anything stuck to the sealing part of the flapper or the porcelain rim it bears against that might prevent complete sealing; or
2) you need to check the chain or whatever it is that connects the flush lever to the flapper (sometimes they get a kink in them and the flapper doesn't go down all the way); or
3) you need to get a new flapper ($5).
Toilets are pretty simple,,,you should be able to prove to yourself that the flapper is at fault by pressing down on it and forcing it to seal: the tank should fill up with your hand holding the flapper in place (don't worry...the water is clean!).
Please report back after you investigate further.
(One other less-likely possibility: I just fixed a neighbor's toilet with this symptom. The nut on the inside of the tank that holds the flush handle in place was a little too tight and the handle would sometimes stay depressed, so I backed it off about a quarter turn so it could move easily and return to the normal position.