I'm not so sure that we need to be this extreme about critiques. A critique is a detailed analysis and discussion of a literary work. I think that, too often, people are encouraged to shift from a critical analysis of a story's merits and faults to being critical, or "inclined to find fault or to judge with severity, often too readily."
We speak English. We have so many words to choose from. You can clearly express thoughts about a story's strengths and weaknesses without being brutal, and without being too soft and fuzzy. There's a middle ground. For the purposes of this post, I'll think in terms of critiquing a short story, but this stuff should all be applicable to novels, essays, and even poetry.
On to my tips!
First, read the material carefully. Read it twice if it's short enough. I feel like this should go without saying, but since everyone has a chronic shortage of time, I'll say it anyway. You're not going to be helpful AT ALL if you just skim over the story. Treat it with the respect you'd want given to your own story, or don't critique it.
Take the time to think over your reactions. Jot down your thoughts about what you don't understand. Try to see what effect the writer seems to be going for. Think about what would help her write the story she wants to write. Your job is not to turn it into the story you want to read; it's to help the writer accomplish her goals.
Think about what works well in the story, because it's encouraging for writers to get positive feedback about their strengths.
Start the critique with the positives, and then get to what didn't work so well about the story.
State the negatives honestly, but not brutally. For example, instead of "Page three sucks. It doesn't make sense when Character A says [whatever] to Character B. No one would say that," you could say, "I don't understand Character A's motivation to say [whatever] to Character B on page three. It seems unrealistic. It might come across better if you set up Character A's motivation earlier, or had him say it a different way." With the latter you're expressing almost the same thought, but doing it in a way that won't trigger the writer's defensive "rejection of message" reflex. Instead of saying that the passage objectively sucks, you're saying that you subjectively don't understand it, and that is something it's easier for the writer to deal with. It makes the writer want to help you, not hit you.
Make suggestions, not demands, if you're going to recommend specific ways to change the story. For example, instead of saying "You need to do [whatever] to make this work," try suggesting "What if you did [whatever]? I think that would help to accomplish [the thing the writer seems to be trying to accomplish]." It doesn't take much longer to say it that way, and it's more likely to get results. People generally don't like being bossed around. BTW, recommending specific ways to change the story is not strictly required. Your job is to help identify weak spots, not necessarily to prescribe solutions. Your way of fixing a story problem might not suit the writer you're trying to help. It's better for her to use her own ideas and style to make changes.
BONUS SOCIAL SKILL: At the end, reiterate the positives about the story, because it's way too easy for the writer to forget the good things that were said and focus on the bad. Besides, if the writer gives up on the story out of dejection, then all of your time spent reading and critiquing the story will have been for nothing. It's in your best interest to be encouraging if at all possible, unless you enjoy wasting your time.