Gmail is a free e-mail client provided by Google. The beta version, which was only available by invitation, was released in 2004, and Gmail was released to the public in 2007. As of August 2009, there are 150 million Gmail users worldwide, which means there is a good chance that someone you know has a Gmail address. There are a few ways to easily find a person's Gmail address.
Use an already known form of communication, such as the telephone, alternate e-mail address or regular mail, to get in touch with the person and ask them if they have a Gmail address. This is by far the easiest way to obtain that information. Not only is it polite to ask, it can serve as a heads-up to expect an important e-mail for the person in question.
Search for their name using a search engine such as Google or Bing. If they have a social media profile, blog or website, you may be able to find it with a search engine. Depending on their privacy settings, their full profile or blog may not be visible or they may not have listed their e-mail address.
Use a web service dedicated to searching for public information. E-mail Finder or Spokeo are two examples of websites that can search for Gmail addresses based on a first and last name, city, state or other information. Websites like MyLife or Intelius have a broader scope, searching for more than just e-mail addresses, but they will still work.
Search within your own Gmail account for their Gmail address. Perhaps the person in question e-mailed you in the past, but you did not add them to your Gmail contact list. The reverse is also possible, you may have e-mailed them in the past but forgot to add their Gmail address.
Ask a mutual acquaintance or known associate if they would feel comfortable telling you the person's Gmail address.