Grenade use is easy. You can just primary fire and throw them but unless your target is prone or doesn't see the toss then they have plenty of time to get out of the way. So you should cook your grenades, in essence burning off some of the fuse before you toss.
I'll go over handling for both teams, since each side's grenade behaves differently. The fuse on both sides lasts for about 5 seconds.
Starting with the Germans: their grenade starts to cook as soon as you press the fire button. Pressing primary fire gives you a normal toss with the maximum range. Using alt fire will give you a underhand toss that has about half the range. In both cases holding down the fire button will extend the range you throw the grenade and the grenade is not thrown until you release the button.
As for the Russians: their grenade's fuse does not start when you press primary or alt fire. The type of toss is the same, primary fire for a long overhand toss and alt fire for the short underhand toss. The fuse will not start until you release the grenade, however, UNLESS you press the other fire key. For example, you hold primary fire to begin your toss, if you press alt fire before throwing you will hear a click and the fuse will begin to burn. Once you have started the fuse the grenade handles like a German one.
To cook the grenade you hold the button and count off (I use One-One-Thousand, Two-One-Thousand, etc.). Generally I will throw on the count of 3 or 4, otherwise you will get an airburst right in front of your face or the grenade will go off in your hand.
Usually it is worthwhile to take the time to cook your grenade as it gives little to no reaction time for your opponent. The disadvantage is that you have a live grenade in your hand for 2-4 seconds so you are fairly vulnerable and need to be in cover until you pop up to throw.
