Shuttle or taxi from port of Dublin to city center

As you aren't allowed to walk directly off the ship the cruise company should always provide a shuttle into town, but this is usually to one drop off point at Merrion Square, in my experience.
You need to check with your cruise company what their plans are, although many don't tell you until the night before to protect excursion sales.
In any event the company provides a free shuttle to the dock gate, which is where a taxi will pick you up. Although it isn't a taxi rank all the drivers know when a cruise ship is due, and will be lined up expectedly.

The scheduled bus from the ferry terminal to Connolly and Heuston Stations (the #53), closer to the sea, doesn't come that way out of the docks.

From the dock gate you can walk to the LUAS tram terminus at The Point. There is a sidewalk and it's a safe area, but also a very industrial area. It's my standard way out of the dock complex- walk in and out for the tram.
Once you reach The Point you are in redeveloped docklands so totally different. From there it's about another 15 minutes walk to the EPIC- the Emigration Museum and the Jeanie Johnston.

Thank you!