Analyze the drawing with fresh eyes. Do not read the title of the piece or the artist's statement. This may sway your opinion of the piece.
Find the imagery in the piece. This means you should determine if the image is a portrait, landscape, still-life or abstract. This can be very telling of the message of the piece -- if there is one. How does the artist use principles of design -- balance, contrast, emphasis, motion?
Decipher the style of the piece. This can mean impressionist, realist or many other styles. Basically get an idea of what the artist was going for. For example, when looking at a Picasso, you can tell it is a portrait, but it is abstract. When looking at Frida Kahlo's self portraits, you see a sense of realism in that she truly captured herself as she was.
Look for use of color. Color can bring emotion to a drawing, such as anger, sorrow or happiness. If there is no color, look at the use of shading for clues to the emotion. Color can also reveal cultural influences.
Observe the use of line. If the lines are fluid and organic, the drawing may have a calming effect. If the lines are rough and jagged, the intensity will show through. If there are no lines and the image is primarily shading, observe the depth of the piece created by these layers.
Read the artist's statement and the title of the piece. See if your perspective corresponds with the artist's intent. Remember that a good critique is not a criticism of the work, but a constructive statement of elements that work and don't work. It is in no way a stamp of "like or dislike," though your opinion as a viewer is valuable. Interpret why the artist created this work. Define his view of the world. You can appreciate different kinds of art, but that doesn't mean you would want it in your home.