If you have not reviewed the Hacker Methodology write up now is a good time to check it out. It will provide you with a much better overview of how we are logically gathering intelligence in order to create a solid basis for the later phases of hacking or penetration testing.
In this overview we're going to learn about some of the common uses of nmap, go over a few of the switches or options and how they work and then wrap it up with an example of a scan.
Disclaimer: nmap is considered to be recon for further action and can be taken as hostile intent. It's a grey area between illegal and not, depending on how good of a lawyer you have. I recommend ONLY using this in our Hacker Lab. Used incorrectly it is VERY obvious when you are scanning.
There's a reason why Digital Ocean is listed under my Recommended page. You can spin up a server in 60 seconds for less than a dollar a week. What this means to the aspiring hacker or network security professional is that a very minimal fee you can host a variety of quick cloud services such as e-mail, VPN, webhosts, application servers, FTP etc.