There is only one way to fully explore the rural Northwest of Ireland and that's by car. Once here, you can always rent a car at Ireland West Airport Knock or Sligo Town. But if coming from Dublin, many opt to rent from one of the bigger companies at the larger airports. If arriving from Northern Ireland, there are rental agencies aplenty in Derry or Belfast, but be sure to tell your agency if you are planning to cross the border.
The roads between the larger towns are fairly well maintained and signposted, but go slightly off the beaten track and conditions can vary from bad to dirt track. As long as you're not in a mad rush, this can add to the delight of your journey. This is rural Ireland, and if the scenery doesn't make this blissfully clear, then the suspension on your rented car certainly will!
In the Irish-speaking areas, signposts are written only in the Irish (Gaelic) language, which can be confusing. Make sure that your map gives both English and Irish place-names.