In Ireland you can experience all four seasons in a day. There can be damp, chilly stretches even in July and August, the warmest months of the year. Layers are the best way to go. Pack several long- and short-sleeve T-shirts (in winter, some should be thermal or silk), a sweatshirt, a lightweight sweater, a heavyweight sweater, and a hooded, waterproof windbreaker that's large enough to go over several layers if necessary. A portable umbrella is absolutely essential, and the smaller and lighter it is, the better, as you'll want it with you every second. You should bring at least two pairs of walking shoes; footwear can get soaked in minutes and take hours to dry.
The Irish are generally informal about clothes. In the more expensive hotels and restaurants, people dress formally for dinner, and a jacket and tie may be required in bars after 7 pm, but very few places operate a strict dress policy. Old or tattered blue jeans and running shoes are forbidden in certain bars and dance clubs.
If you're used to packing things or stowing dirty clothes in plastic shopping or drawstring bags, bring your own. About the only place you can find the latter here is in the closets of better hotel rooms (for on-site dry cleaning and laundry). Plastic bags carry a 22¢ government levy and can be sold by supermarkets, but it's illegal to give them away. Most stores use paper bags or recycle boxes.