A few common methods depend on the specific chair design and the type of swivel base being used to attach a swivel base to a chair. One approach involves custom-building a swivel base for a new set of chairs, as demonstrated in the first video. This typically involves constructing a sturdy base and attaching it to the chair frame using screws or other fasteners. Another method, as shown in the second and third videos, is to replace the existing chair base with a swivel base kit. These kits can be purchased and installed yourself, usually involving removing the old base and attaching the new swivel base using the provided instructions and hardware. It's important to follow the specific instructions for the chosen swivel base kit and ensure proper stability and attachment to maintain the chair's safety and functionality.