How do I start a Social Network from scratch?

In the real world, social networks not based online which should qualify with your vague condition, ("I do not want to use any website."), consists of friends, coworkers, and family. The quality is up to you. How you maintain said friendship and work relationships. How much give and take enters into the equation will shape the level of quality of this social network.

On the other hand, if you are asking the overwhelming question on how to make your version of Facebook, Diaspora*, or any other online social network site, you are going to be surprised to find out that you will be having a very difficult challenge ahead of you.

How much computer programming do you know? Any IT and server experience? You will have to build and design your own site or if you have a lot of money, an entrenpenurial spirit/drive, and a knowledge of marketing psychology.

To paraphrase a well worn adage used at luxury stores around the globe, if you have to ask the question then you probably don't have the skills to pull it off.

If that doesn't discourage you from your venture, start learning as much server programming as possible. Maybe take a business course to boot in order to prepare yourself in terms of how to handle the up and coming infrastructure challenges that come with new businesses.