If you want to allow people to register to your site, just follow these simple steps.

1. Login to WordPress Dashboard and Go to Settings > General.
2. Just check the Anyone can register checkbox.
3. Set the New User Default Role (Subscriber, Contributor, Author. Editor, Admin) from the select menu.

If you are going to allow registration for the public, never set default role as Editor or Admin. You can read more details about WordPress user roles and their capabilities at the WordPress Codex.