Best way to get from Dublin to Edinburgh

Flying...otherwise it's trains. ferries and buses.

Flying is the obvious, sensible choice

"Best" is always a subjective term.

There are multiple flights daily.

Or the surface option takes about 12 hours, and is seamless. Bus (coach) from Dublin Busaras at 0645 to Belfast Europabus Centre. Bus connection from there to the ferry terminal. Straight on to the ferry, off at Cairnryan, Scotland where another bus (coach) will be waiting to take you to Glasgow (Buchanan) Bus Station, connect there into the double decker bus (coach) which runs every 15 minutes .

Arrive at 1839 (but if on time should be 30 minutes earlier)

Cost £33 from Belfast (ferry inclusive- the ferry alone is £32 if you book it independently) + £9.50 for the bus from Dublin to Belfast.

Fly....unless your backstroke is really good.

Both Aer Lingus and Ryanair offer numerous nonstop flights between the two cities. They take slightly more than an hour.

I say "best" is subjective, because of course flying is fastest. But you see nothing and it is far more polluting to the environment, which is something at least some Europeans (including me) are really interested in. Like it or not climate change is here, some people like me will do what they can to try to at least arrest that change.
And no nonsense about baggage sizes etc.

Actual real locals use the ferries for those and other reasons.

The ferries are good ferries, and on a daytime sailing in July you are never out of sight of land. Unlike flying you also get the chance to eat a proper meal and move around and get fresh air. And on the land transfer part from Cairnryan get to see some quite scenic parts of Scotland you wouldn't otherwise see.

You even have a movie theater on the Stena ferries.

Arguably the faster (and certainly more frequent) land route from Dublin is to Holyhead, then train from the rail connected station at Holyhead to Warrington or Crewe, connecting for train to Edinburgh. That is especially true for those who are not used to long distance bus travel.

Modal choice depends on if you just want to get from A to B fastest, or are as interested in the journey.

Strongly agree with isn31c. I must fly to Europe, but once there my personal rule is to travel by trains and ferries. I'm not in a hurry, appreciate the less intrusive security, and enjoy that I get to see the country and people of the places I visit. Some of my most relaxed and memorable travel experiences were on ferries, seeing the coast of Wales or Ireland reveal themselves, the most beautiful sunrise on the North Sea or contemplating the emotions of young men far from home before landing on invasion beaches.

Strongly agree with isn31c and VAP. There are many carbon calculators online, such as www.carbonfootprint.com, which might be helpful in making travel decisions. Some will only offer a cruise option vs. ferry and give a much higher number than is accurate for a ferry. Find one you like and then see the effects of our travel on the environment. The one thing I adore about being in Europe is public transportation! The scenery! People’s lovely faces! Smell the roses