You can give tickets away to activists using the "Comp Tickets" tab on your ticketed event's manage page.
In the tab you will see a ticket purchase form without any of the credit card fields. Fill in the form (at least first name, last name, email address, and ZIP code are required, plus at least one ticket amount and any required fields on custom form inputs you've added) to send a receipt to that activist with their free tickets.
Comp (or complimentary) tickets given away in this way will count in your ticket totals but not ticket amounts. On reports they will be listed as having costed $0.00.
To delete a comped ticket, you can go to the Latest 100 Activists section of the Tickets tab and remove the submission. You can also remove this action directly from their Activist Record. In both cases, the activist will be removed from the action and they will receive an email notifying them of the cancellation.