One of the biggest flaws of Dublin is its transport.
First of all, there is no underground. Therefore do not think you will get anywhere faster than if you biked.
The fastest public transport is the DART line, a train that goes up and down the city, but more in the East side. There is just one line therefore either you are lucky enough to live next to a station, or you will have to look for a different solution. Even if you have a good location, it costs on average 2.50 euros to go on it. Therefore it can be quite expensive.
Same goes for the LUAS lines. The LUAS lines are like trams but they cost the same as the DART. This time there are more than one. I only know 3 of them but maybe there are 5. They are super slow and in rush hour it is possible to not be able to get on it. London underground vibes.
Taxis are an expensive option but even they do not go as fast as you would like. Once it took me 45 minutes to get to work in a taxi, a drive that should’ve been 20min max! Therefore I do not recommend taxis or driving your own car either, unless you love traffic.
The last alternative is the bike. A lot of people go from one part of Dublin to the other in a bike. If you would have told me a year ago that I would cycle to work I would’ve laughed. Unfortunately it was the case as it was the cheaper and fastest option for me. I didn’t buy a bike, I bought a membership of 25 euros a year to use DublinBikes whenever I wanted to. This is great and I loved the healthy alternative. But you need to be careful with the cars. I was scared as I don’t have a driving license therefore I am clueless when I bike on the streets. Luckily for me there were plenty of other bikers and I would follow them and imitate their ways for driving next to the cars. There are also some cycling paths once in a while which can make a great difference.
Finally, you have your feet. If you love walking then you would be surprise by how fast you can get from one place to the other on foot but it is only recommended if you are walking around the city center. At least for me as I hate walking.