Let's assume you're on a Windows platform and using the Zenmap GUI. Launch Zenmap by clicking the desktop icon or the Start menu link. Here we see the startup screen for Zenmap. There are fields for the target, scan profile or type, and the nmap command line details. The rest of the window has panes for the results, with tabs providing different ways of viewing those results. There is even a network diagram view--nice!

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Simply type in the address, subnet, or range of IP addresses in the target field. Choose the profile that suits the type of scan you want to run. Hit the Scan button. That's it! After the scan completes you can click on the various tabs and items in the results to learn the details of the results. You can save the results of your scan if you like. Of course you can use the command line version of Nmap if you prefer that.
One of the neat things Nmap can do is identify the type and version of operating systems at the IP addresses on a network. This can make it very easy to identify what's there, rather than trying to sort out what's using each IP address manually. Updating IP address lists and diagrams is quicker when you know what's there. It can also sometimes help find old versions of operating systems or firmware on hardware that's out of sight.
Of course these are some of the least sexy uses of Nmap. There is excellent documentation out there and there are even some books that explain in depth how to use it. Good luck with your scans!