Your RSVP question will probably look something like this:

The labels on those checkboxes are the Friendly names of the groups they represent, so the first thing you'll do is set up your groups and give them friendly names.
*You do not need to make these public groups!

Next, you're ready to add your "Add to Group" Field to your registration form. Select Add to Group from the dropdown menu:

Update your Field label as you like, for example: "Will you be able to attend this event?" Then, select the two groups that you just created as your checkbox options:

That's it! Preview your form to see how the friendly names appear in the field:

Next, you can set up an automated message, or series of scheduled messages, to deploy to registrants. Most likely, you'll want to have one automated email to confirm the contact's registration. Then you may have one or two scheduled emails to deploy before the event, and one email after the event to thank them for coming. You can schedule these messages to deploy to the "Event Registrants" group when you set up the form. Scheduled emails will deploy to anyone who is in the group at the time of send.
You can also make sure that you have a registration reminder group (by removing registrants from the group you first invited), by updating your form options:

You can schedule a reminder email to deploy a few days before registration closes to the "Event Invitees" group, and whoever has not filled out the registration form will be sent the reminder.
If you have specific questions on how to customize your event registration form, please reach out to your account representative!