Sept-Oct 10th. Shannon Airport. Not want to drive or long bus tours. Prefer take bus's-trains? Tralee, Dingle,,enjoy exploring towns & nearby, 2 nights each &head up Galway Shannon airp
So, you just want to use ordinary public transport, not sign up for a bus tour or van tour, is that right? If so, you'll be using Irish Rail and Bus Eireann. See https://www.ireland.com/en-us/what-is-available/getting-around-ireland/articles/public-transport/
The Irish Rail intercity map is here. As you'll see, to get around the smaller towns you will want buses. http://www.irishrail.ie/travel-information/station-and-route-maps