Locate the event you wish to issue comp tickets for via Events > Upcoming.
Click "New Order" next to the event. If you do not see this button, then you need to first add registration types to your event.
In the New Order popup, you will see all the registration types pre-filled out. Remove the irrelevant ones by clicking the red X button.
Adjust the quantities and price as necessary. For issuing free tickets, you can either enter a price of 0 zero, or you can click "Comp" on the following screen after creating the order.
For the Guest field, enter the email of the recipient. You will see a dropdown box that will search the database to see if that person is already in the database. If they are, select them. If not, click "Add... [email]", fill out the customer record screen that pops up, and click save.
When the order looks good, click Save. This will save the order as a draft, but will not issue tickets just yet.
Now you should see this screen:
Click the big green Process Order button to issue the tickets. The page will refresh, and verify that the State is Complete, and the Payment is Paid. You can also click on the Tickets tab to see how many tickets were issued.