There are several ways to send a farmville gift. At times when you first launch the farmville application in facebook, the farmville gift screen appears and you can send a farmville gift to any of you facebook friends. If they are not already playing farmville they will have the opportunity to start and become you farmville neighbor.
Another way to send farmville gifts is to click on the Gift link at the top of the farmville application.
If you want to send a farmville gift to just one neighbor, you can click on their icon at the bottom of the application and then click on send gift.