In recent years, the demand for renewable energy has increased significantly because of its lower environmental impact than conventional energy technologies. As a result, wind power is one of the most important renewable energy sources. As land-based turbines have reached their maximum potential, recent market trends are moving into deeper waters with higher capacity turbines. The design of a floating offshore wind turbine (FOWT) foundation poses technical challenges. Mooring design, installation operations and the fact that it is a new engineering field, to name a few. Moreover, as mooring design for FOWT is still at an early stage of development, cost-effective installation remains one of the critical issues. After the FOWT is towed to the site, the mooring lines are hooked up, and one line is usually shortened. This can be performed in three ways: By seabed tensioning, inline tensioning or tensioning at the fairlead. In this investigation, details about mooring installation processes are collected from interviews, academic papers, manuals and videos to investigate differences between mooring system installations and ultimately figure out how pre-tensioning of these systems can be carried out most effectively. This work presents a comparison between these three existing methods for the final phase of mooring installation. To perform a quantitative study, the Umaine VolturnUS-S 15MW floater is considered. Current modelling techniques are expanded to allow for the static simulation of the rotations or sliding at the tensioning device. The model framework is used to find the static equilibrium and tensions at different phases in the installation operations. Additionally, an alternative mooring configuration is proposed with synthetic inserts to verify whether the tension is dependent on the mooring configuration. Finally, the dynamics between the anchor handling vessel(AHV), the FOWT and the mooring chains are modelled as a linear mass-spring system. Vessel responses and work wire tensions are compared against each other for identical environmental conditions and equipment specifications. Based on simulation results, it is found that the seabed tensioner causes little dynamic relation between the AHV and the floater and was not further investigated. Inline tensioning showed to be the method that requires the lowest tensions in the AHV work wire. Fairlead tensioning was found to be discouraged since the high required bollard pull forces. This issue is mitigated by a proposed new concept of fairlead tensioning. When the chain is hauled in from above the fairlead by a vessel crane or A-frame, it is possible to tension effectively without fuel-intense bollard pull.