There are multiple reasons to want Neighbors in Castle Story. Fortunately, there is a system to help you connect with other players and become neighbors.
On the lower-left corner of your screen is the Menu button. This brings up a page with five important selections. The one we want is "Social." This goes to a page with three tabs: Community, Neighbors, and Invite.
Any existing Neighbors you have are on that tab. But to find new neighbors, click Community.
The list there rotates randomly through player names. Click on one to Visit that kingdom. When you get there, look for an "invite" button near the lower right. Click it to ask the person to be your neighbor. If they accept, they will now be on your neighbors list!
There is also an inkwell button, "Wall," where you can leave a message for that person, and see if they already know a ton of people posting.
During your visit to any kingdom, neighbor or not, you will see up to 5 Hearts floating above buildings, etc. When you click them, you raise your own Social Rating, which means your name will appear on the list more often for others to select!
It is best to look on the Community tab for lower-level players, most of whom are also looking for neighbors. This will also help you find people who are eager to trade Gifts.
When you visit a neighbor, you get a small reward - a few Coins, an experience point, or an energy point. When you click hearts, the neighbor gets a small boost, either an experience point or an extra drop from that resource. It also makes their kingdom sparkle!