they need to sign up, or just refering them is enough?
You actually don't even need to do either. Click the Refer button when logged in on your mobile device, choose email/facebook/twitter, and then simply hit the back button. It will thank you for referring someone and offer to do it again. I did this and got my gift card.
Oh and you don't need to be a Verizon customer either. This is a free $5 card to Starbucks for anybody that can be had in under 2 minutes.