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Find a village. Build more houses with doors in the village. Build gardens for the villagers. Trade with the villagers.
Villages can be found in the plains, desert, and Savannah biomes.  The village needs to have at least 2 villagers. Be patient.  Villages are not always easy to find.  You may have explored for a while before you find one.  Use the map you get at the start of the game to keep track of your location. You can also cure zombie villagers by first throwing a Splash Potion of Weakness and then feeding it a golden apple. Make sure it doesn't come into sunlight until the zombie villager has completely transformed, or it will burn up. Villagers will mate as long as the total population of villagers is less than 35% of the number of valid doors (rounded down) in a village. A valid door is any door where one side of the door leads to a room with a roof, while the other side leads to the outside.  To increase the number of doors in your village, you can build a single structure with multiple doors. To add more doors to a village, build a single structure with multiple doors. Villagers love to grow crops.  Most villages already have a couple of gardens already built.  You can build more to make the villagers more likely to be willing to breed.  To build gardens, find a well-lit area and dig a trench next to dirt blocks and fill the trench with water.  Then use a hoe to till the dirt blocks.  You can plant seeds or vegetables in the dirt blocks, or allow the villagers to do it themselves.  You can also throw food to villagers.  Villagers become willing to breed when they have either 3 bread, 12 carrots, or 12 potatoes in their inventory. To craft bread, select a crafting table and place three wheat stalks in any row of the 3x3 grid.  Drag the bread into your inventory. Trading with villagers is the primary way to make them willing to breed. Different villagers have different items they are willing to trade in exchange for a different item.  You must have the items the villager wants in your inventory to trade with them.  Trading with same villager multiple times unlocks new items the villager can trade. Trade with the villager until a new trade appears to make it willing. Afterward, subsequent trades have a 1 in 5 chance of making the villager willing again. Green particles appear when a villager has become willing through trading.  Being willing to make will not automatically make the villager seek out a mate.  Two villagers that are willing to mate must be in close proximity. After they mate, the villagers are no longer willing and must be made willing again.