If you want to invite friends, family, colleagues, readers or anyone else to sign up on the same Mastodon instance as you, there's a handy invitation system which does exactly that:
1. Click on the "invite people" link in the bottom left corner of the page. (If you're on the multicolumn interface, click on the "invite people" link at the bottom of the Getting Started tab.)
2. Choose your invitation settings (uses and expiration date)
3. Click "Generate"