If a property owner is installing a fence independently, without assistance from bordering neighbors, the fence should be installed inside the property line. Surveys often vary by a few feet, and there could be later disputes.
Neighbors who disagree with fence placement have been known to dismantle offending structures. Let your neighbors know about your plans for a fence.
Local ordinances may regulate how far inside the property line a fence must go. Laws vary in individual jurisdictions, so check ordinances in your area before installing a fence.
Ordinances may regulate fence height, materials that can be used, and colors for fences.
Some states and local jurisdictions have shared or common boundary fence laws. These allow a fence on the boundary line between properties when both property owners agree to it and share the cost of building and maintaining it.
In this case, both property owners can use the fence. Without this agreement, a property owner must have a fence inside the property line, and bears the cost of erecting and maintaining the fence.
The adjoining neighbor cannot use the fence at any time in the future.