Having the house already wired with Cat6 is just like having the house already wired with electricity, or phone wires, or plumbing.
You still need some company to provide service to the house. An ISP.
Just like the local water company or electric company.
You need a router capable of a WiFi signal only if you have some WiFI only devices. And you probably do. An iPad, for instance.
How to set everything up? Completely unknown. It all depends on how it is actually wired. There are probably ethernet ports in most of the rooms, all terminating back to a central point.
When the installer comes to hook you up he can maybe, probably figure it out.
Whoever wired this should have left a detailed schematic of where everything goes.