As much as Call of Duty is usually a team game featuring objectives, for a lot of people their kill/death ratio is more important. If you want to check it yourself in-game, here's how to do so o Call of Duty Vanguard.
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K/D is just a point of pride really - a stat you can show off to your friends. Otherwise, it doesn't mean a whole lot, as fun as it is to keep an eye on it.
How to Check K/D in Vanguard
You'll first want to head to the main lobby menu in CoD Vanguard, since you can't check K/D during a match in Vanguard, unless it's for that one game.
From there, head to the Barracks tab, and scroll down to the Records section of it. Not only will that section show how much time you've spent playing Vanguard and your Win/Loss ration, but it'll also show your your K/D.
However, it's not called K/D in Vanguard. Since the game is a little more generous with what it counts as an elimination, it's also more generous with K/D. Instead, it is call Elim/D, where some of the kills you get post death or for inflicting a lot of damage on a player but not getting the final blow also count.
You'll find your exact K/D or Elim/D number in the bottom left of the squares on the Records page. You'll be able to to track it from game to game to see how it changes.
It's also worth noting that you can check out your Elim/D ratio by mode and by weapon. That may give you a good idea of what weapon to focus on using or which mode best fits how you play.
As you unlock more weapons and attachments, you'll likely improve and see your K/D fly up, so keep an eye on it.