to pick a religion that you already have in a city, as your state religion, you do that in the religious advisor. there's a button on the screen but i use the F7 key to get there.
when you hover over each religion at the top of that advisor screen, it shows you which cities would benefit if you pick that religion as your state religion. you make your decision by clicking up top and then i think "convert" is the word at the bottom of the screen.
religion changes follow the same rules as civics switches, 1 turn of anarchy if you're not spiritual, 5-turn waiting period to change it again whether you're spiritual or not.