Your computer's IP address and more advanced settings can be found within the network settings. However, there are free websites that can show you your public IP address instantly.
To find your private and/or public IP address manually, find System Preferences and look under Network. Then, choose Advanced Settings where you'll find options for TCP/IP. This is where you'll find your private IP address.
The easiest way to find your public IP address, if you have no DNS or VPN masking it, is to simply type "ip address" into a Google search bar. Google itself will likely show you your IP address. Or, you can choose one of the free websites, such as whatismyipaddress.com, which will display it instantly.