How to get everybody on your religion

[LeSphinx]

Yes you can build shire in the conquered cities.
The city must be the Holy city of the religious: look at the religious advisor to see which city is!
LeSphinx

 

[André Alfenaar]

One cheap way to get to some free conversion is by building trade routes to your own and AI cities. Discovering Sailing works very well for this! (Religion spreads via trade routes; you don't need missionairies or open borders for that!)

Sailing is usually I go for after I have got to Monotheism. A newly founded coastal city is immediately connected to your trade routes. Mind, however, that the route along which this trade is going to be happening has to be explored. There is no trade over unexplored area.