Hi! Just curious... 

Let's say the Game Designer doesn't know how to draw/sketch. But he/she can provide references, rough sketches to the artists, etc. so that they can come up with the final sketch.

1. So, how is all this added in the game design document? Should the game designer just add references from other games, movies, etc and write a description of how the expected look and feel of the game should look like? Is this the right method?
2. Is it the game designer's fault even after providing the references and rough sketches to the artist and he/she can't come up with the final artwork? 

1. Sure, why not?

2. It sounds like a communication problem to me. Do not worry about where to place blame. Maybe blame doesn't need placing. In fact, why not just throw blame into the trash entirely?

3. Moving this to the Game Design forum. Yes, GDDs require writing, but GDD writing is nevertheless a Game Design task.  

14 hours ago, JoAndRoPo said:

So, how is all this added in the game design document? Should the game designer just add references from other games, movies, etc and write a description of how the expected look and feel of the game should look like? Is this the right method?

You want as much detail as needed in order to to convey a clear idea and understanding to everyone reading the document. Add as many references and sketches as needed.

14 hours ago, JoAndRoPo said:

Is it the game designer's fault even after providing the references and rough sketches to the artist and he/she can't come up with the final artwork? 

What is the reason the artist can not come up with the final artwork? If the artist isn't able to draw that's one issue, but if the artist isn't on the same page as the game designer regarding concepts then you're most likely going to run into issues. The same applies to if the designer doesn't communicate clearly to the artist. I wouldn't worry about "blaming" anyone, I would spend more time fixing the communication problem.

If someone tells me "I want you to draw a tree with bats flying around, and put a thick fog in the air with a full moon." Then they reference a Castlevania image, and the artist draws this but then the designer comes back and says, "well... I need the tree to be more broken up, less branches, and maybe a tomb stone in the background with a dug up coffin... Oh and don't forget the moon light needs to go through the fog." This is a communication issue... For starters, how big is the tree, what kind of tree, how big are the bats, how many bats, ect.... You can nit pick an artist for days if you wanted to.

I'm not sure if you're a designer or artist, but you 'must' be very specific when telling any artist what you would like done as a designer. You also need to allow for that creativity to flow because every artist has their style as well. If an artist's creativity gets clamped down, or they're having to re-do work over and over again, you'll be looking for a new artist fairly quick, and that problem wont go away if unchecked.