The Operating system on the computer is MAC OS.

 Click on Apple icon the top left corner.
Go to System Preferences.
Then go to Network.
If you computer is wired to the router then you will find the option Built in Ethernet.
If your computer is wireless then you will see Airport.
Click On Built in Ethernet if the computer is wired.
Or click on Airport if the computer is wireless.
Click Advanced option.
You will see TCP / IP tab at the top.
If you go to that tab you will find the IP address on the computer.

This is the IP address of your computer.
If your computer is connected to the router then IP address will be like 192.168.X.Y.
( X and Y may be any number )
You will also see the Router number.
This is the IP address of your router / Modem.
Note down the IP address  and Router number.