May to mid-September is by far the warmest and generally the driest time of year, relatively speaking (Ireland is often chilly and damp). The absolute best times to visit are probably from mid-May to the end of June and during the month of October—the weather is good for touring, and there are likely to be fewer tourists. The rest of the summer is fine, though a bit crowded. In summer, temperatures generally fall in a range of 59 F/15 C to 68 F/20 C.
Winter days can be drizzly, cold and short (the sun sets around 4 pm), but because of the Gulf Stream, the temperature seldom falls below freezing, averaging about 45 F/7 C. Winter is also an opportune time to meet the Irish—few tourists are about, and you can easily find conversation at the local pub. No matter when you go, a light raincoat or Windbreaker is essential, and you'll need a wool sweater and a jacket or coat, especially at night.