Here are just a few tips to keep in mind when critiquing someone else's work:
Critique the technicals.
Exposure.
Is any area overexposed or underexposed? If so, can you say why you think that happened? How could the photographer prevent this problem in the future?
Focus.
Is the main subject in focus? Is it sharp focus, or a "soft" focus? Is the focus appropriate for the situation?
Depth of Field (DOF).
Is the DOF shallow or deep? Does the DOF work in this shot, or should more (or less) of the photo be in focus?
Lighting / White balance.
Is the light soft or harsh? Does the type of lighting enhance or detract from the things in the photo? Is the white balance set correctly? Is there a yellowish, orangish, or greenish cast to the photo?
Critique the composition.
Centered vs. "Rule of Thirds".
Is the main subject in the center of the frame? Is it on a third? Somewhere else? Does the chosen composition work, or would you have done something differently?
Fore, Middle, and Backgrounds.
(Most applicable to landscape photos) Does the photo contain all three? If not, do you think it would be better if it did?
Cropping/Framing.
Is there wasted empty space is the photo? Should the crop have been tighter? Is it cropped so tightly that important parts of the photo have been cutoff?
Color / Tonal Range.
What type of colors do you see? Did the photographer use a lot of primary colors? Secondary? Complementary? Are the colors too vivid? Not vivid enough? If you are looking at a B&W photo, is there a true black, true white, with a large tonal range in between, or is the photo too "gray"?
Diagonals, S-Curves, etc.
Did the photographer make use of any visually-interesting elements, such as diagonal lines or S-curves?
Leading lines.
Do the lines and overall composition make you want to look deeper into the photo? Is your eye drawn into the photo, or out of it?
Dark vs. Light areas.
Are there too many bright areas? Too many dark areas?
Balance.
Is the photo "balanced"? Would it be better if there were other objects or other light/dark areas in the frame to improve the balance? If the photo is off balance, is there a reason for it?
How does it make you feel?
Even if you are a beginner, you are certainly qualified to critique based on these questions:
What mood do you see in the photo?
Do you think this mood is what the photographer intended?
Does it make you happy? Sad? Angry?
Did the photographer succeed in telling his/her story with the photograph? Why or why not?
Do you like the photo? And, more importantly, say WHY you like the photo, or why you don't.
Would you hang this photo on your wall? Why or why not?