Dublin's pub life makes it really well-suited for a celebratory long-weekend. While probbaly outside of the typical backpacker's budget given the exchange rate, it's still a relatively affordable city. Great meals and drinks can be yours for €10-15.
Walk! Dublin, like most older cities, is designed for walking. Wander through the changing neighborhoods, stroll along the river, zig-zag across the bridges. If your feet get tired, there are public buses and street cars. Buy a ticket at the machine if there is one, or just pay onboard.
The biggest of all the tourist attractions, but the view at the Gravity Bar on the top level makes it totall worth it. Meander your way around the museum which is shaped like a giant pint glass. Be sure to stop at the Academy to learn how to pour the perfect pint of Guinness. Take it upstairs with you to enjoy the view!
I didn't even know about The Book of Kells until I got to Dublin, but it's definitely worth an hour or so to check out the ancient, intricate text dating back to the 9th century. The colors, even after all these years, are stunning. Plus any bookworm will love the Long Room in the Old Library at Trinity College which is included in the tour.
Irish stew made with Guinness is a must-have. Get it at a pub with a pint. My favorite is at O'Neill's. Swing by in the evening for some live music for peak Irish. Pro-tip: Any Irishperson will tell you never to pay more than €5 for a pint. If you're being charged more, the pub you're in is too touristy!
Rain gear. You'll be thankful for shoes that keep your feet dry and a rain jacket or umbrella when it suddenly starts to pour, especially in the spring.
Sure, you can try to practice your Irish Gaelic, but English will do just fine.
Ireland is designed for road trips. Take a day trip out to The Cliffs of Moher and swing by Galway for a small-town vibe. If you want to tick off another country while you're tehre, take a quick bus or train ride up to Belfast, Northern Ireland and visit the Giant's Causeway.