The ownership of a structure by a world (Blue, Green or Red) is displayed on the WvW map. Each structure contributes a certain amount of points towards the owning server's war score.
To take ownership of a structure, a world must kill the lord NPC (the Veteran Supervisor, Champion Tower Lord, Champion Keep Lord or Legendary Castle Lord depending on the type of structure) in order for the claiming ring to appear. They must then kill all enemy NPCs and players inside the ring, and stand inside until the structure is captured. The lord NPC is located at the center of each structure, so the attacking world will have to break through the structure's defenses first to attempt a take-over.
Structures can be claimed by a guild. Claiming puts the guild's emblem onto the banners hanging from the structure, and causes any active Art of War Upgrades to apply to players near to the structure.
Every guild can claim a maximum of one structure per map for their guild. They can do so by talking to the Guild Claiming NPC of an unclaimed friendly structure. If the structure is just taken, the guild that dealt the most damage to Guild Claiming NPC can claim it. If the privilege is not used, other guilds will be able to claim 4 minutes after the capture.