Wordpress - Wordpress Multisite - When a user signs-up on main site, how to add the user to a subsite

Run add_user_to_blog() after user creation.

You can hook on user_register() to get newly created user ID and pass it and any conditional assignments to your callback that runs add_user_to_blog().

I complete @hwl's answer:

Most of the times, in a Multisite instance of WordPress, user registration includes an activation step.

In this case, it is necessary to hook actions on wpmu_activate_user; actions hook on user_register will be ignored. For instance:

my_function($user_id)   {
    // to add a user to main site (id=1) as a subscriber add_user_to_blog can be used
    // more info: https://codex.wordpress.org/Function_Reference/add_user_to_blog
    add_user_to_blog( '1', $user_id, 'subscriber' );
}
add_action('wpmu_activate_user','my_function',10,1);