Socka said:
when will a city become a holy city?
Be the first to discover one of the "religion" techs. Meditation (Buddhism), Polytheism (Hinduism), and Monotheism (Judaism) are all in the ancient age. If you start with Mysticism (the Arabian, Aztec, Incan, Indian, or Spanish empires), it's not too hard to end up with either BuddJew or HindJew (no slur implied, those are the gamer names for founding Buddhism or Hinduism along with Judaism).
After that, you can shoot for Code of Laws (Confucianism) or Philosophy (Taoism) in the classical age.
Finally, you can shoot for Theology (Christianity) or Divine Right (Islam) in the third age (Medieval?).
The later four religions come with a free missionary, for a chance at spreading your religion. Note that I've had about a 20% chance (guesstimate) of the missionary failing to establish the religion in a second city.
Once you've established a religion, one of your cities is selected at random to become its holy city. (In one game that I heavily cheated, I established all seven religions in my nine cities: 3 cities with two each, and 1 city with one.)
You've now got a holy city. What can you do with a holy city? The only benefit that I can see from a holy city (that is independent of having the religion in the city) is you can use a Great Prophet to build the Shrine.
The Shrine provides one gold for every city that has your religion, and provides Line of Sight (effectively, a permanent observer) in every city that has that religion--though that may only be the case if the religion is your State Religion. It also allows you to turn three people into "priest" specialists.
The benefits of religion that accrue to any city having the religion (including the Holy City) are: the ability to build temples (one temple for every religion in the city; each provides happiness and culture, as well as the ability to turn one pop point into a "priest" specialist), monasteries (one for each religion in the city; each provides a short-term ability to build missionaries, as well as a short-term boost to research--this disappears with The Scientific Method, I believe, but you'll be able to build missionaries with one of the Religious civics), and "cathedrals" (one per X temples of a religion, can put in any city that has that religion; a big boost to culture, a boost to happiness, and the ability to turn two people into "priest" specialists).
Note that the priest specialists are not cumulative across religions. If (as happened in my heavily-cheated game) you have seven religions in one city, seven temples, two cathedrals, and two shrines, you don't get the ability to turn 15 people into priests, only 1 (for having at least one temple) + 2 (for having at least one cathedral) + 3 (for having at least one shrine) = 6. And I don't recall those priests actually using up a pop point, so they could be free (but at the expense of seriously bumping up your Great Prophet production in that city).
More information than you asked for, but I hope it helped.