Dublin has a cool and wet climate, with rainfall and temperatures moderated by the water. Peak tourist months are July and August, when the weather is at its best. May, June, and September are also relatively pleasant, and you can probably get better deals since there aren't as many tourists. The average high temperature during the summer is just shy of 20C. It's also the driest time of the year, and thanks to the high latitude, there's a lot of daylight.
Consequently, winter days are very short. Temperatures are cool, rarely dipping below freezing or getting above 10C and snow and sleet are common. It's dreary woo -- weeks can go by without seeing the sun. Dublin can be depressing from late November through March. December is the wettest month, receiving 7.3cm on average, though rainfall is distributed fairly even throughout the year.