Every claim is already controlled by a faction. To acquire one for yourself, you have to take it from someone else. To seize a claim, tell the GM which claim on your map your crew intends to capture. The GM will detail the claim with a location and a description and will tell you which faction currently controls that claim. Or the GM might offer you a choice of a few options if they're available.

If you choose to ignore the roadmap paths when seizing a claim, the GM might tell you that you'll need to investigate and gather information in order to discover a claim of that type before you can attempt to seize it.

Execute the operation like any other score, and if you succeed, you seize the claim and the targeted faction loses the claim.

Seizing a claim is a serious attack on a faction, usually resulting in -2 faction status with the target, and potentially +1 status with its enemies.

As soon as you seize a claim, you enjoy the listed benefit for as long as you hold the claim. Some claims count as turf. Others provide special benefits to the crew, such as bonus dice in certain circumstances, extra coin generated for the crew's treasury, or new opportunities for action.