Today Verizon has tweeted out that pre-orders for the Samsung Galaxy S4 will begin tomorrow (4/25). Keep in mind that this would be ordering it from Verizon directly. Earlier this week, Best Buy stores started to allow reservations of the Verizon device, as they did not have pricing info either.
So if you are looking to be one of the first with the Galaxy S4 running on Verizon, be sure to check back tomorrow, as their pre-order page should be live.
source: @VZWnews (Twitter)