when you say modem, do you mean an DSL modem or a standard modem style of thing?

Normaly yuo have a switch, and a modem. someimes a switch is refered to as a hub. A router is a gateway device between the internet and your private network, if you have more than one computer.

Normaly you connect the DSL modem to your router, and your router manages the connection to your ISP. The router is in turn connected to your switch (or it is a switch as well).

For WiFi (wireless) you have an access point. this can be part of the router as well.

In my case I have a modem (DSL) hooked up to a switch/hub. I have a access point for wiFi that conencts to the switch. The base station can be a router as well, but i have configued it to be only a access point. Only cause I had problems getting it to work as a router (dont know why, maybe a firmware issue).

Give me a rundown on what gear you have, and tell me which type of internet service you get as well as how many computers you have and how they can connect (or how you would like them to connect).