...Publicly...in Ireland (or elsewhere.)
Whether you're on your own or with a group, chances are at some stage, you may need a public transportation option. Even in Dublin, the Luas is handy for getting from one point to another and it's easy enough to figure out.
Your best friend for using public transportation abroad is going to be google. You can plan your route before you leave your accommodation and take a screenshot on your phone. All you have to do is select the transit option when you search for directions. You'll get information on timing, which bus number to take; you'll also know how much walking you'll have to do between stops and locations. Of course, that's an option that's handy even at home because let's be honest...does everything ever really run on time everywhere...?
If you're spending a lot of time using buses and or trains to get around, it might be wise to invest in a Leap card instead of having to keep the right change constantly on hand. Likewise, the Oyster card can be used in London. Do some research before you head out and see what kind of options you have!
For longer trips between cities and counties, getthere.ie is a super handy tool for keeping an eye on Bus and Rail times throughout the country. They also run a lift share service, but we'd be more inclined to suggest you use the public options.
Another alternative way to get around the likes of Dublin and other large cities these days is the use of on street bike hire, pick up in one location and drop off at another. Information can be found at the pay stations with the bikes. They're often sponsored by the likes of Coca Cola, and although they're very straightforward to rent and use, sometimes stopping into an actual rental spot is worth the extra effort.