To look at responses to invitations, select your party from the drop down menu under the checkout icon. Click the Guest List icon. Here, you can choose to add your guest's details/email address or print the invitation to hand in person.
You can manually check which of your guests will be attending in the Guest List tab of your Party dashboard.
For emailed invitations, your guests will be emailed an invite that includes an RSVP button. From here they can RSVP yes or no, and this will automatically update your guest list.
If guests RSVP in person you can manually tick the yes or no buttons in the Guest List tab of your Party dashboard.