How do I add Pokemon to my team?

Teams

Once you hit level 5 and try to enter a Gym, you can choose from three teams: Team Valor (Red), Team Mystic (Blue) and Team Instinct (Yellow). Each team may be tied to a respective Kanto legendary bird Pokémon (e.g. Instinct is yellow, and has the icon of Zapdos).

_{(source: pokecommunity.com)}

Note that the official website states that you ‘cannot change Teams at this time’. Maybe this restriction will be removed later, but make sure you’ve talked to your friends which you should choose before you jump on a team!

Source

I'm fairly certain that Team here refers to the different Factions within the game.

Each faction fights over control of a Gym, and rids control by 'weakening' that Gym by defeating it.

Since Gym access and battles become available at level 5, I presume that this is the time that you will get to choose which Team/Faction to fight for. It was the same way in the predecessor of Pokemon Go, also made by Niantic.