Claiming a system can be valuable itself, as it secures the system with a clear indication of rules you can set. Expanding your faction either from a military perspective or through structures that can help your faction grow is also an important aim, and is required to undertake certain faction activities such as fabrication or research.
Some structures only require a prefab to build, such as the buoy, but most structure will require several structure components to construct. Before any of this can be attempted however you will first need to secure a ship with the construction role such as the Civilian Guild Engineer class ship. The Engineer requires the Construction Craft skill to use which is within the negative range of the sensitivity factor. If you are yet to realise this skill you should focus on completing missions that decrease your sensitivity factor such as "Raw Material" missions.
With the Engineer ship you can begin building and claiming structure. The aforementioned buoy only needs the buoy prefab to build, this prefab can be found at most systems that trade parts as its a low level component. With this components within the hold of an Engineer ship you can build the buoy in any system that is not claimed. To perform the building, open the engineering window and choose the option to build next to the blueprint of the buoy. The buoy requires no power to operate so can therefore be used to claim systems in remote regions.
For structures that require several components you will either need to purchase these components or fabricate them at a factory.
Most structures also require power to operate. Power is shared across the entire system so power structures can be built on any body within a system. The most basic power structure is the solar collector which can be placed in orbit.