how to get from Dublin to Galway?

Are you asking for a driving route? What is your definition of "best"? Fastest? Most scenic? Easiest for a beginner left-side driver?
The M6 appears to be a direct route, passing Athlone, which is on my list of places to visit. Castle, old pub and nearby Clonmacnoise.
The train goes the same way and also stops at Athlone.

ok, thanks for focusing my question! Has anyone taken the train from Dublin to Galway? Or is there a public bus? would a tour bus be better to actually see the sights?

There is a direct bus from the airport. There is probably also a bus from the city center, but I don't know why anyone would choose that over the train unless it stopped somewhere the train doesn't. The trains in Ireland, though somewhat limited in their range) are very good: clean, comfortable, inexpensive if you buy tickets in advance.
I am not aware of a tour bus that would take you one way from Dublin to Galway. You could hire a private driver, I suppose. There are tour companies that do single- and multi-day tours out of Dublin that include Galway. Rabbies and Paddywagon are the two main tour companies, but there are others. There are also tours departing from Galway.

I've taken the train from Dublin to Galway. It only takes a couple hours. It departs Dublin from Heuston Station, which can be reached via tram. The Galway station is an easy walk into the city centre.

Galway Ceannt railway station has this year been expanded from 2 to 5 platforms to cope with future expansion and extension of the Western Rail Corridor, and a new 2nd station entrance added.

Yes there are also buses from central Dublin-some of which are airport services.

Booked on the day at the station the fare from Dublin to Galway is €30.45, booked on line it is €16.59 amendable up to 60 minutes before departure.

You’ve received good information here.
🙂.

The pub in Athlone referenced above, I believe, is Sean’s Pub. It’s reputed to be the oldest pub in the country (or county or universe).

I’ve done the trip between Dublin and Galway (Oranmore) many times, as recently as twice in 4/26.

The train can be particularly fun when there’s a match in Galway. It’s also a pretty ride. Bus is fine, too.

We took the CityLink double-decker bus from the Dublin airport to Galway. It passed through downtown Dublin and at one stop, some passengers got off, while others got on, then it was non-stop from there to Galway. Sitting in the front window up top, we got a mini-tour of Dublin, followed by great countryside views. Having just flown across the Atlantic overnight, we also both got in a bit of a nap. Restroom onboard the bus, too. All very easy, comfortable, quick, and affordable, and I’d challenge any other method to be “better.”

We did finish our trip with some nights in Dublin at the very end, but the mini-tour by bus at the start was fun.

thank you everyone for the insights! I so appreciate your time and experience!

I just returned from Ireland last night.
I took the train from Dublin to Cork and back, also some small commuter trains around the Cork area, and they were all just fine.
I’m sure it goes to Galway also.
The trains were all on time to the minute.
Clean enough and options to buy food for the journey at the stations as nothing on board.
Buy advance tickets as the service is very busy and well used.
I loved Ireland!