All you have to do is go to your local Target and have a Target Mobile employee check your upgrade eligibility status on your Sprint, Verizon or AT&T account.
And that's it! That is officially all you have to do to receive your $5 gift card. You will likely also be informed of current promotions, so take this as fair warning. But if you're not eligible for an upgrade, don't sweat it-- nobody can push you into a sale.
Just an FYI: If you do have an upgrade ready, a $150 GC is given out to iPhone customers, and a $100 GC is given out to GS7/GS7Edge/GS6 customers. This is possibly going to change tomorrow, so I'll likely update my post later tonight.