How do you breed villagers in minecraft?

Villagers automatically breed when certain conditions are met.

First, make sure there are more beds than there are villagers. Second, be sure there is a bell in your village, otherwise they will not stay in the area and will wander in search of a bell. Third, be sure there are profession blocks that new villagers will be able to use (only one villager can be bound to each profession block). Also, make sure the area is safe, as villagers will sometimes not breed if there is a risk of death. Finally, make sure there is a wheat field, and at least one farmer villager. The farmer has to collect wheat to make bread, which will then be distributed amongst the villagers. When you see a villager throwing bread to another one, this means they are breeding. Watch for baby villagers, and try to ensure that they live to adulthood!

The basic conditions under which villagers decide to breed are (from the top of my head) as follows:

1. The two villagers that you intend to breed need to have food (carrots, bread, pumpkins etc.) => easiest to achieve to have carrot farm around and have that regularly drop carrots onto you villagers.
2. The "village" needs to have more beds than villagers. Village in this case means the technical thing the game recognises as a village. This term does not mean that you need houses etc.

Unless you want to mass produce villagers for something like a trading setup you are fine with some villagers in a fenced in place that is well lit, so zombies cannot come in. Give them a few beds and toss them a bunch of food. You might as well make one of them a farmer and have them grow crops themselves.

All these changed with the village and pillage update (1.14 for Java-Edition) to what you see above. You used to have to have sky access or a bunch of doors under a roof instead of the beds.

For more details you should always go to the official minecraft wiki