Public Mobile is in Beta meaning that they are limiting the number of SIM cards they hand out. The only way to obtain one is to sign up with your email to be a Beta tester essentially and in roughly 3 weeks or greater you will get an email stating you've been welcomed to join the beta project and you can contact public mobile with a unique pin to have them mail you a sim card free of charge
At this moment, please note that Public Mobile is currently in BETA. They are temporarily accepting new customers only by invitation.
New customers must join the BETA phase at http://publicmobile.ca/en/on/beta
You will be contacted by email within a few weeks. Once you receive your invitation code, you will be able to subscribe on Public Mobile and order a free of charge SIM card.
For now, there is no faster way to subscribe on Public Mobile. They are in BETA to make sure everything works perfectly before the official launch.