To be able to invite users you have to have "Admin"-permissions for your community. If you have admin permissions you'll find the "Manage" option in your profile menu.
There are 3 ways to invite users to your community:
1. Send an invite to a given email
In the Admin panel go to Admin > Community. You'll find the button "Invite Users" there. Enter the Email addresses of the people you want to invite and click "invite" to send an email invitation featuring a registration link for your community. This works with and without activated payments.
2. Create a user and send them a password creation link
You create the user yourself under Admin > Community > Create and then assign the plan. The user has to reset his password first so he can log in. This works with and without activated payments.
3. Send a registration link for a specific plan
Go to the plan you want to invite the person to under Admin > Monetization > Plans > click on the plan. At the top, you will find the direct link to the plan which you can copy and send to your new user (also works for hidden plans). This works only with activated payments.