Routers don't come with software, they have everything they need built-in, and you don't install anything on your computer. You have no 'server' either - each machine connects directly to the router, and each machine can do so without the need for any of the others to be turned on.
If you have an ADSL connection via a phone line this router connects to it via a modem. You don't need to connect a computer directly to the router, although you can do so if you wish, via ethernet cable.
Otherwise, your computers connect via wireless network cards.
Perhaps you can explain what this software is that you say you have to keep installing?