Start with the basics. What is the modem make\model. Look for a tag on it. From that, along with who your service provider is, folks here might be able to start you in the right direction.
Most service providers these days provide a modem\router combo (most also charge a $5-12 monthly rental fee). The best visual clue is, a modem will have a WAN + 1 LAN ethernet port. A Router will tend to have a WAN + 3-4 ethernet LAN ports. The Wide Area Network port (WAN) connects to the cable feed into your home, the other ports can connect computers and other devices to the local area network (LAN).
If it is a wireless router, there will generally be a WiFi SSID and Password printed on the label as well, this is the default and can be changed in the web UI. These are generally reasonably secure, but if someone has access to the device in your home, they can get the WiFi credentials off the device (similar to putting a sticky note with your password on your computer screen).
If you look at the Network properties in System Preferences, the LAN IP address and router IP address will appear, something like 192.168.1.1 (router) and 192.168.1.2 (Mac). With any web browser on the Mac, type in the router address (
http://192.168.1.1) and a login screen will appear. Google search the router login or manual to get the default login. Once in, for security purposes, change the password to something only you would know, and remember. From there, all kinds of fun becomes available as to configuring your network.