This should be moved to the Variants board.
I take measures in my IRL tournaments to decrease the effect of luck, but only the ones that are the most visible. I allow players to stack their deck before the game begins so they get to determine their opening (I lol-ed so hard when one player going first decided to get a T1 Noble Brigand just to mess with people. Seeing the look on her opponents' faces was priceless
) and I remove certain cards like Rebuild, Cultist, and Urchin that can lead to games that don't feel good. It's a token effort I make to prevent complaints like "Roadrunner got a 5/2 on that board so he won, there was nothing I could do" and get people to leave the tournament with a warm fuzzy feeling.
There are plenty of other sources of luck in Dominion that mean much more that I make no attempt to compensate for, and people don't care. I try and make the format of my tournament compensate for the fact that there's luck in Dominion and hey, a good person has won all of my tournaments. I can only play a certain numbers of games IRL given time constraints, and the real solution is to play more games anyways. Oh well, I do what I can. Dominion has luck, what can you do? You can increase your whining skills, sure, but really, who out there can really rival me on that?
When I'm playing IRL and I get a really good 5/2 opening, I'll usually offer to my opponent to just take a 4/3 instead if they want. If they get the good 5/2 and offer the same to me I'll usually just let them take it. I've found that most attempts to decrease luck in Dominion don't really do very much so I'd rather just try and feel better.
Online, well you just DWI and play lots of games.
There, I've contributed to the thread.