Critique (noun): an act of criticizing; especially: a critical (see critical) estimate or discussion (a critique of the poet’s work; an honest critique of her art).
There is a body of thought that considers the act of submitting your work for a critique to be akin to requesting that you be flogged in public. That seems like a harsh judgement, but I understand the sentiment behind it. After all, the very essence of the critique is that it should involve your precious work being poured over, dissected in fine detail, and commented on. Faint of heart, please do not submit.
Many writers do, though. Submit, I mean. The reason for this apparent masochism is that having your work critiqued is one of the finest ways to gain the insight and inspiration needed to improve your writing. Assuming, of course, that you don’t instantly tear the critique into tiny pieces, and then resort to rending your garment in despair.
What follows is a personal and random collection of thoughts on the art of the critique. Health warning: these should not be relied upon as a blueprint for critiquing the work of others. Though I am sure that will become obvious as you read on.
Never critique someone’s work if they have not asked you to do so. This is especially the case in the US, where you always have to bear in mind that many citizens have access to guns.
Always try to provide at least one positive comment in your critique, which will allow the author to cling to the last vestiges of her or his self-respect. However, you should be aware that following this by three hundred negative comments will almost certainly undo any good you might have done.
Detailed comments in the margin of the MS should never start with phrases like “You must… ,” or “You need to ..,” or anything else which could be interpreted as an order barked in a strident voice. A gentler approach is more likely to evince a positive response. Use phrases like “I would … ,” “You might consider … ,” or “Have you thought of … .” It is also appropriate to rewrite a phrase, sentence or paragraph to illustrate your point. Do not, however, even consider rewriting the entire piece. This is the writing equivalent of eating peas with your knife in polite company.
Never be tempted to comment “LOL” when you see a spelling mistake or a word used wrongly. Also resist the desire to say “FFS Edit your damned work before you submit it,” or anything in a similar vein. If you find yourself in this frame of mind, I can recommend the application of a fine Scots malt whisky as a remedy.
Always be specific and constructive in your comments. Phrases like “This is rubbish,” “Get yourself a thesaurus before we all die of boredom,” and “If I see another dangling participle, I shall have to pay a visit to Mr Shredder, and we don’t want that, do we?” should be avoided wherever possible. In the same way, describing the author’s plot as “puerile,” or remarking that his main character “Lacks substance to the extent of being invisible to the reader,” is bound to lead to heartache.
If your critique is related to the activities of a writers’ group, then you may also have to provide verbal feedback. It is preferable that this follows the general thrust of your written feedback. However, do not be tempted to go through your detailed comments line by line. This will almost certainly have the effect of inducing terminal somnolence in the rest of the group.
Finally, if the author has requested specific feedback on some aspect or aspects of the piece, do not be tempted to do anything but ignore her or him. Everyone else will, and you do not want to be responsible for breaking this fine tradition, do you?
Happy critiquing!
stuarthaddon 
Sage advice indeed!