The Iarnrod Eireann/Irishrail timetable can be downloaded here.
Two companies operate non-stop coach services from Dublin to Galway, so that there are departures every half hour.
Gobus (leaves Dublin at a quarter past the hour, leaves Galway at a quarter to) Timetable here.
Citylink (leaves Dublin at a quarter to the hour, leaves Galway at a quarter past) Timetable here.
The last coach from Galway to Dublin on Saturday is at 19.15 The last train is at 19.20. Train tickets can be substantially cheaper if pre-booked online.