Okay, so first you need to Identify them.
It's pretty easy to do.. If you haven't finished the game, the jaeger is the one that kinda looks like a captain of a ship just like this one,


Now, if you have finished the game, the one with yellow and green clothes will appear, just like this one, below.

Ranged attacks:
These units use both pistols and grenades.
First of all, if they are close to you, (in range for a melee strike) and they try to use their pistols against you, you can either:
1) Use a human shield
2) Just strike them once with a melee weapon. Doing so will cancel their attack, forcing them to block you.
When they use grenades:
Well, your only option is to run straight to them, making them throw their grenades close to them, doing significant damage.

Melee attacks:
Well the secret here is to just let them come to you.
When they're attacking, Press E to block the attack. Now, you'll notice, if done correctly, when you block their melee attack, the screen goes blurry, and the game slows down for some seconds.
Now all you have to do, is press SPACE, to break their defense, and then spam left click.

Now for the secret I promised:
You probably have noticed that these units are immune to kill streaks. You can't take them down with a single blow.
BUT,
There is a chance. (Thankfully, cause it gets kinda tiring when there are too many of them....)
You'll notice, that when you take down many enemies at once, or you fire your pistol, SOMETIMES, very RARELY, Jaegers look a little bit of afraid, they back off, letting their guard down for just a second or two. IF, you are quick enough, you can take them down using kill streaks. When they do that, (letting their guard down) They're no longer immune to killstreaks. Now, I won't guarantee that this will work every time, sometimes it will work, sometimes it won't. It's a cool feature that I noticed, and now,
go out there and ♥♥♥♥ them all up. Go on a rampage! :D
I hope I helped you enough!
This below is how a Jaeger that got "scared" after a killstreak/ "unique" kill with tools or something.
You can clearly see, he's unbalanced and his body stance is not right for an incoming attack. So therefore he is no longer immune to killstreaks for a second or two. Again, it is not guaranteed that it will work everytime.