I had to build missionaries and manually spread them. For some reason, it didn't spread on its own. I've had open borders with almost everyone too. And a few trades. What should I be doing to make them spread on its own?

AFAIK the main factors are, Road network, proximity, cultural level of the city with the religion, and whether the target city has a religion already.

My civ was isolated on a small continent, so they weren't conencted with others by road. I did spread it to a few civs on the other main continent, but didn't seem to help.

I think being a trading partner with the foreign country helps. I've noticed that my religions spread more quickly to nations to which I am exchanging resources. I haven't looked to see if individual trade routes are involved.

That's the missionaries use for.

Regards,
Arto.

You should also build the shrine for your religion as it spreads religion more quickly

Never seems to be a problem with me. Sometimes I might get Taoism and the enemy in the next turn converts to it, while it does not spread to any of my closer cities. Weird eh? (the cities have no religion)

Religions do spread on their own, even to other continents when there are trade routes, but only very, very slowly, perhaps four or five cities in other civs during a game at Normal speed. Holy Shrines are reputed to help the spread: the "four or five" includes that effect. Spread in your own civ also occurs, usually in new cities (which can also pick up "foreign" religions in a few cases), but not often.