In general the west of Ireland is not well served by public transport and since many of the most interesting sites tend to be a little off the beaten track hiring a car is probably the most convenient approach.
If you do hire a car a good map is a must and it is usually worth while to get an up to date guide book if you plan to visit regions not covered by your own research. Also bear in mind the Ireland is in principle a bilingual nation so you will see road signs in both English and Irish (Gaelic).
For those of you from countries where people drive on the right it is worth remembering that in Ireland people drive on the left and it takes a bit of getting used too. Also bear in mind that many of the rental cars are manual gearshifts so if you prefer automatic cars make sure to specify when renting.
Clare's main towns are connect by regular bus services and there is a mainline rail station in Ennis. The only public transport too and from Shannon airport are buses .