Thank you for an excellent question. Not too many years ago, and perhaps still in some parts of the world, a Freemason was not allowed to approach a man about joining the fraternity. He lived his life in a quiet, distinguished and honorable fashion that, hopefully, would set an example and attract men of similar character. Through observation this man would be seen to associate with other men of respectable character and the observer would eventually express an interest in the group. However, at this point the Freemason was still not allowed to discuss the fraternity with him. He was required to wait until the man expressed interest three times before he could answer any questions. Fortunately, this tradition is no longer strictly followed in most parts of the world.
Today, you can introduce yourself in a variety of ways. Some Grand Lodge jurisdictions have online forms where you can request someone contact you. Most Masonic Lodges are listed in the local telephone directory. If you know someone who is a Freemason just ask him about it. Or, find the local Masonic Lodge building and stop in and say hello. There's no reason to be shy. We're just a group of men who have promised to do good and be good, and we're always glad to meet men who are interested in the same.
However you are introduced to Freemasonry the process of becoming a member takes some time, and everyone goes through a similar process. No one is 'Grandfathered in.' Just because my Grandpa was a Mason doesn't mean I will automatically be granted membership. Men are accepted or rejected because of who they are, not because of who they know or are kin to.
Basically, the process begins with you getting to know some of the members of the fraternity and letting them get to know you. It is not, and should not be, a quick and easy process. Two members will be required to vouch for your character by signing their names on your petition. Three other members will serve as an examining committee, and assuming they find favorably, they too are essentially vouching for you as a man of character. Then, the Lodge members present at a regular meeting are required to vote on your petition. As I said, it is not an easy process but nothing truly worthwhile in life ever is.