Before you activate your ticket make sure your e-mail address is verified with Steam. For instructions on how to do this click here
From within the Dota 2 client click Store
located at the top of the main menu. Once you're on the Store page you can then click on the Backpack
Locate the International 2013 Ticket from the backpack and Right Click
on it. Select the option which says Use.
You will then receive a popup which will ask you if you're sure you want to register the ticket.
Once you click Yes you'll receive a message letting you know the registration details will be sent to your e-mail.
Once you've activated your ticket from your backpack you'll receive an email from Steam Support. Within the email there is a button labeled Click here to claim your ticket.
This button will pull up a PDF of your print out ticket, this must be printed out
and presented at the door of the event to redeem your pass.
Additionally the top of the Dota 2 Main Menu will now display a ticket icon letting you know that you're registered for the International.
Clicking on the ticket will give you the option of re-sending your registration information to your verified Steam email address.