There is nothing bad about a city having a religion (exeption at [1]).
It is very good through most of the game to have as many of your cities as possible wiht your state religion, as those cities get 1 extra happiness and bonues dependant on your religious civic.
The more religeons your cities have the more remples and monastries they can build, and this is often a good thing.
When you discover a tech that gives you a religion it is founded in a random city. To spread it around you have to build missonaries (or you could wait for "free" spread like the AI does, but that is very slow).
To build missonaries a city must have;
That religion
Either a monastry, or you must be in the organised religion civic (a very power civic when you are not at war).
It does not use food. It MAY cost you money.my normal use of it is to go to a high production city that does not have too many other religions and spread religion. Then you can build a monasry if needed and get on with spreading it about.
You are welcome. Hang around, you shall learn loads.
[EDIT] Iforgot [1]
[1] the only disadvantage I can think of is that if the city has a chance of revolting to a neigbours civ, then if that city is his state religeon, and that religion is not your state religioun) then it will have a higher chance of flipping. Can anyone think of any other?