Every device connected to a network has an IP address. It is a unique identifier that locates your computer or Mac on the network. It is most likely that your Mac connects to the internet through a network or router; which implies that you have (1) a local IP address that identifies the Mac on the local network (router) and (2) a public IP to connect to the internet. This short tutorial explains how to find these addresses on your Mac.
Finding your local IP address
Finding your local IP address is really easy. Click on the Apple menu > System Preferences > Network and then select the connection you are currently using: AirPort (wireless) or Ethernet (wired).
If your Mac is connected (Status: Connected) then your local IP address will appear on the top right corner of the menu.
NB: You can also find your local IP address using the ifconfig command. Go to the Application folder > Utilities > Terminal and execute the ifconfig command.
Finding your public IP address
The public IP is provided by your ISP, you can find it in the configuration page of your router. Enter the address (192.168.1.1, 192.168.0.1 or 192.168.2.1) provided in your router's manual in the address bar of your web browser and press Enter. Enter the username and password when prompted. Search for a section named Router/WAN Status, your public IP address (Internet IP Address) is listed there.