To all, need help with finding answer to my problem; The fill tank for my toilet is draining water very slowly and is causing water to re-fill periodically in tank when it drops below the fill line and below the ballon in tank. I have an American Standard model toilet. Thanks in advance for any suggestions!

Replace the flapper.

To all, need help with finding answer to my problem; The fill tank for my toilet is draining water very slowly and is causing water to re-fill periodically in tank when it drops below the fill line and below the ballon in tank. I have an American Standard model toilet. Thanks in advance for any suggestions!
Thanks for advise!

Robkelly's post while short is correct. First let's see if it's a bad flapper or simply a adjustment. Take your finger and run it around the flat part of the flapper. If it's wavy or has rough spots then it's bad and should be replaced.
If the flapper's OK then check the linkage between the flapper and the flush lever. 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 untill 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. 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.. Good luck, Tom