In order to obtain a Religious Victory, you must make your Religion the predominant Religion for every other major civilization in the game. This means not every one of a civilization's cities must follow your Religion, just the majority.
While your Religion will spread passively simply by settling near other players, it is your Missionaries and Apostles who offer the best chance at victory.
TEAM RELIGIOUS VICTORY
To win a Team Religious Victory, Religions founded by the team must be the predominant Religion in every other civilization. The dominate Religions can be of any combination as long as the Religions were all founded by team members.