Chaos Cosmos Browser is included in the installations of V-Ray, Corona, and Vantage, and does not require any other specific actions. You can access the Cosmos asset and material library from your V-Ray Corona or Vantage UI menu. See how to place 3D assets from Cosmos in your Vantage scene here.
If you open the Chaos Cosmos Browser for the first time, you have to log in with your Chaos credentials. To do so, click on the Sign-in button and enter your Chaos credentials. Then open the Chaos Cosmos Browser, download and import the 3D models, materials, and HDRIs you plan to use.