There's a lot of Call of Duty WW2 info to digest post reveal, but getting on the beta is probably top of everyone's list right now.
Currently, this is a private beta which can only be access via pre-ordering the game. So that's a down side, although you can bet there'll be a public open beta at some point.
However, if you absolutely can't wait and you've pre-ordered the game already (don't pre-order video games) then it's just a case of heading here with your code to preorder the game on the platform of your choice. (You'll need a COD/Activision account if you haven't already got one.) If you buy through the PSN or Xbox Store you'll be "automatically validated to participate." If you by via retail then you should get a code on your receipt.
There's a few T&Cs involved. Like the fact that it's only on PS4 and Xbox One (sorry PC). That said, the details state "actual platform availability and launch date(s) subject to change." Various platforms might all start on different days as well so let's hope you chose wisely. Whatever happens you're guaranteed a minimum of three beta days.
And, just in case you were getting your hopes up, "experience will not carry over from the Private Beta." Like that ever happens.