All you have to do is go into Verizon and show them you ID badge or have them all you employer to verify that you are actually employed their and they will add it to your account. Hope that helps that is what I had to do
You can fill out the form online to get your discount here:
You can also go into the store, but they will just be doing exactly what you could do online from your computer. Typically they need a work e-mail address to verify. Just know that it will not be instant, depending on where you are in your billing cycle you may not see the discount until 2 billing cycles from now.
I would say to do it online if you have an email address from your employer. It applies instantly. If you do it in store it will take 2 to 3 billing cycles and you will NOT get a retroactive discount.