Most commonly by the geographic area one lives in or has ties to. Otherwise, some people like to choose a team that wins a lot or, on the opposite side, an “underdog” team that never wins.
Yup, that’s me. I grew up near Seattle, so the Mariners and Seahawks are my teams for baseball and football. I got into soccer after I moved to Utah and the Sonics left Seattle, so Real Salt Lake and the Utah Jazz are my teams for soccer and basketball. We didn’t have a hockey team growing up, so I went for the Vancouver Canucks for hockey, but now I’m going for the Utah Hockey Club.
I used to really like the As because of Moneyball, and if I’m watching a game with other teams, I go for the underdogs (e.g. for the Premier League, anyone other than Man U, and I’m partial to Arsenol because they have a cool name).