Head to Inkopolis Tower (it's the really tall one) and choose Regular Battle to get started. Playing online lets you level up and earn in-game coins for new gear.
Regular Battle is one of the four multiplayer mode categories in Splatoon and Splatoon 2, along with (in Splatoon) Ranked Battle, Squad Battle and Private Battle. In Splatoon 2, Squad Battle is replaced with League Battle. It is accessible from the beginning of the game and has no ranking system used for matchmaking; it is more casual in nature due to this.
Turf War: The only mode playable in a Regular Battle. Turf War battles consist of two teams of four players each. Both attempt to cover the most ground with their team's colored ink in three minutes. When the match is over, Judd determines the winner based on the amount of covered ground.