Between April 29 and May 6, you’ll be able to access Turf War, Ranked Battle, and even Salmon Run – you’ll even be playing against people who have the full game. So if you’ve wanted to convince someone to get into Splatoon 2 – it’s a perfect time for it.
During the demo event, you'll be able to jump online* and fight it out in 4-on-4 Turf War battles with friends and other players who own the full game. You can also try out Ranked Battles and the Salmon Run co-op mode.
Just note that you'll need a strong internet connection and a Nintendo Switch Online membership to participate in the event. But if you don't have a membership, don't worry: You can try it out for free!
Get a free trial for Nintendo Switch Online
Once you download the special demo from Nintendo eShop, you'll receive an e-mail with a download code for a 7-day free trial for Nintendo Switch Online. To activate it, please enter the code into Nintendo eShop. It doesn't matter if you've activated a previous free trial—you are still eligible for this trial, too.
Update: The download is now available, credit to silverrat23
Missing this important bit: