You get neighbors most easily when you are in the County/State/National/World Fair

Weekly competition: click on one of the other 5 players and it will show info on them and allow you to send a Neighbor Request. Picking higher level players can help the most, but at the same time they may not want to be your neighbor (they are looking for higher-level

Neighbors too) ideally, You should get at least 10 of the free sprinklers built somewhere on the edge of your farm, so that people come for the water and you get some too!

If you have friends playing Farmville 2, you can invite them as neighbors as well -- if they are already your friends on Facebook, they do get treated differently than "strangers" in some situations.