 (Friendly addendum: telling an author her or his work melted your brain into a puddle of gibbering glee is also a wonderful review.)

Some readers are more gifted with review and response than this, and they are to be saluted.  One will never have a more valuable review than one that goes through the tale point by point, remarking what does and doesn't work, and using metaphor and simile to compare one's story to the greatest works of fiction.  These reviews are rare.  Do not feel bad if you never leave one or receive one; that would be like feeling sad because your review of the latest "Pirates of the Caribbean" installment was less detailed than Ebert's.  "I loved it!" is just as valid a review as a two-page essay on one's use of lunar imagery.  It's also easier to read.  Do not decline to leave a review simply because you are not in the mood to give in-depth feedback, and please do not think you will come across as a lesser reviewer because of it.  Your feedback is desired and appreciated regardless.

If you are in the mood to give a story the fine-toothed comb approach but don't know where to begin, here are some starting points:

How well the author captured the "voices" of the characters.  That is, could you hear the characters speaking those lines?
How well the author structured the story.  Did the story have a traditional structure?  (Rising action to a climax, and then a quick fall and an ending.)  Was the story non-traditional? (Ex: Time sequence intentionally out of order, a mood piece rather than a plot-driven story.)  Did this work for you, or did it leave you uncomfortable and wondering what the author was trying to do?
How well the author handled the subject matter.  Was the piece humorous or serious, and did the author maintain a good tone for that subject?  If the story was longer, did the author strike a good balance between lighter and angstier sequences?
How well the author managed to achieve her/his goal.  If the work was AU, did the author make the AU believable for the duration of the story?  If the work was supposed to adhere closely to canon, did the author manage to hit the right pieces of canon and slide the story into continuity?  Did the plot make sense?
How well the author handled other pieces of the story.  Were there original characters introduced, and if so, did they come across as useful additions to the story?  Did the author overuse or underuse any particular technique?
Does the story feel complete?  There is a difference between a great story begging for a sequel and a story that is unfinished.

I should stress that this list is neither complete nor compulsory.  It is merely a suggestions list for anyone who'd like a jumping-off place to spread their critiquing wings. 