I have no idea how you'd do it either, so I've never really tried. Every team that I am a fan of I grew up as a fan of the team, and developed a connection to it at a very young age. This will sound incredibly cheesy, but I don't feel like I really "picked" any of the teams that I follow - I got into them at an early age because my dad/family was a fan, so they kind of picked me. I guess the only exception to that was the Nashville Predators - they became a team in 1998, when I was 11. So I guess I wasn't born into liking them (or hockey generally), but I was still young and became a fan because I felt like they were "my team" since they were a Tennessee-based, southeastern US team in a sport that was not all that popular here.
I think I could only see myself picking a team if I developed some kind of personal connection to one (e.g., I moved over there and became a fan of a team close to where I lived, became friends with someone who was a huge fan of a team, etc.). When I first started paying attention to soccer as a kid Man United was on their run and I remember watching some games (when they rarely came on) and wanting them to win, but that was pure bandwagon stuff.