When I'm explaining in my GDD how I want certain 3D animations and characters to look, do I just have to explain in a detailed way what I want it to look like? Is there anything special to it?

Well, what is the description for? Are you planning to hand it to an artist and say, "Here, make this."? Or are you planning to use the document to sell the project to potential volunteer team members, or to an investor or publisher? Any piece of writing has a purpose, and it will be good writing if it accomplishes that purpose

As in, when putting things in my GDD about how a character should look when throwing a grenade and during certain animations for NPCs like while they're talking.
For example, could I just explain "Curling your left hand so the back is facing the ceiling/sky, with the grenade between your palm and fingers, you bend your lower arm until it's straightened and facing the ground, then pull your arm back," etc.
Is there something special you'd have to say relating to the process of creating 3D art?
I suppose I would be handing it to an artist on the team (if the team is assembled, I haven't finished the GDD itself yet, so it may be a while).

I'd go with a less specific and more descriptive approach. Animators tend to like reference material, be that videos, or people actually acting things out in the office. The description of "Grenade Toss" is easy to look up matrerial for. So, you need less specifics on the mechanics of an animation, as a reference video is the faster way to explain anything difficult here. What you should be describing is the feel of the overall animation, and the specifics needed for gameplay. This should cover things like:
What characters are we animating? Is this synced to some other animation, like "cave troll: eat imp" and "imp: be eaten by troll".?
What is the minimum and maximum time limits for the animation? is it related to another animation (the troll example above)?
What animations is this related to? You need to let the animators know what the previous and next animations are, so that they can get everything in the right poses for smooth blending. Is it blended with other animations like walk and run would be blended for a smooth speed transition?
What part of the animation is used? Is this an upper-body-only animation? full body?

For your grenade toss, consider the following:

Soldier: Grenade Toss -> From/To Standing Idle -> Grenade toss using the left arm. Remove grenade from belt, and perform a quick pin-pull with the right hand and overhand toss using the left arm. 60 Frames.
vs
Soldier: Grenade Toss -> From/To Short Wall Crouch Cover -> Awakard Grenade toss using the left arm. Soldier is scared from approaching enemy and fumbles to use his right hand pull the pin before finally succeeding and standing then lobbing the grenade over the wall with the left arm. 90 Frames
vs
Soldier: Grenade Toss -> From Door Cover Left to Stand Idle -> Using right hand hand signal team of grenade, then pull pin, and lob through doorway with left hand. Animation should be time-synced with "Soldier: Door Breach Shotgun Right", who is actually opening the door for the toss. 180 Frames

Thanks for the great answer!
Some things I'm wondering now: is it suggested to tell just how many frames are to be used in the animation and how many frames are there per second? Does that depend on a setting in whatever you're using to make the game (UDK I suppose)?
The grenade wasn't actually a 'grenade' per se. It was a more unique grenade, called an Outlet, where you tap the top and a loop like a yoyo string materializes around your finger. So, you throw it with a bowling-ball-toss motion, where you bend your lower arm until your arm is straight, pointing at the floor and aligned with the side of your body, pull it back a few more inches, then swing forward in a straight motion, bend your arm forward, and let go just under the crosshair (the game is a First-Person-Shooter, so you'll have a crosshair).
I'd simply put that once you hit right-click, your character pulls out the Outlet and taps it, materializing the string loop. Right click again, and he then commences the throwing animation I explained above. I also put "after three fourths of a second, the grenade should have been thrown" or something similar to that. Maybe I should list it in frames instead..?
Once again, thanks for the helpful answer!

EDIT: Forgot to mention it's upper-body only and you can do it while moving, crouching, etc...I suppose I should mention that, too?

Thanks for the great answer!
Some things I'm wondering now: is it suggested to tell just how many frames are to be used in the animation and how many frames are there per second? Does that depend on a setting in whatever you're using to make the game (UDK I suppose)?

For starters, your animation team should be standardized on a specific rate of animation (like 30fps) that is usually based on what the tools you are using are going to actually export.
Secondly, yes, you probably want to be very specific about the animation times. If the animation in question is just flavor, like an idle, then you can ignore timings. Anything that is gameplay related though, you should carefully think if the timing matters. Providing specific times will allow the animators to best tune the final animation to look good. You can fix minor timing errors by just toying with the playback speed, but it will make many animations look awkward if the adjustment is large.

Consider a punch. Does it have windup to it? maybe 1/2sec to let the user know a big hit is comming? Is it a user controlled punch that should feel responsive? maybe it should hit within 3 frames? What type of finish does it have? fast? follow through? etc....

I also put "after three fourths of a second, the grenade should have been thrown" or something similar to that. Maybe I should list it in frames instead..?
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Frames, seconds, doesn't really matter. Whatever is easier for the animators. At work we have Maya, and the animation timeline shows frames.
What matters is that you are specific. I'd say your description should change to "Make grenade release from the hand on frame 22.". Remember, some artist / designer / programmer will have to come back to all this at somepoint and connect the animations to the game, complete with events that have to match specific frames in the animation.

The grenade wasn't actually a 'grenade' per se. .......
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Again, carefully pick a reference. You mention a bowling ball. Is that the right look? maybe a underhand soft-ball pitch? It is a lot better to find a reference video or a easy search term so the animator can find reference material. If you can't find that, be very specific about the description, and have them mock up a really rough animation so you can make sure the big motions look right before they polish in all details.

EDIT: Forgot to mention it's upper-body only and you can do it while moving, crouching, etc...I suppose I should mention that, too?
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If the animation can only be run from specifc starting anims, make sure the animators know so they can get the initial pose and ending pose right. Remember, all the animations have to match within some tolerance, or you will see noticeably strange behavior when blending between them. Sometimes you can fix this with a long blend, but to feel responsive, many animations require you to quickly blend over only a few frames.
If the animation is blended with other animations, and thusly only affects part of the body, let the animators know. For instance many FPS games have upper and lower body segments so the run/crouch/jump animations can be seperated from the switch gun/use gun type animations.

The grenade wasn't actually a 'grenade' per se. .......

Again, carefully pick a reference. You mention a bowling ball. Is that the right look? maybe a underhand soft-ball pitch? It is a lot better to find a reference video or a easy search term so the animator can find reference material. If you can't find that, be very specific about the description, and have them mock up a really rough animation so you can make sure the big motions look right before they polish in all details.

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I suppose a yoyo would be a more appropriate look for the Outlet, but an underhand soft-ball pitch may be the best for the motion the player will take when throwing.
I know I only quoted a small part of your post, but that doesn't mean the rest didn't help me.
Thank you very much!
Is there any post that might serve as a reference so game designers can research the basic things they will need to know about most every aspect of a game (programming, 3D art, sound, music, artificial intelligence, etc.)? That way I won't have to bother GameDev.net with a "noob's" questions ; )...at least not too much.
By that I mean the things like blending and just what you need to explain to certain members of the team you plan on gathering when the GDD is finished.