Go over the work completely before beginning your critique. If you're noting a critique on a manuscript, read the entire manuscript before making a judgment. Questions that come up might be answered if you'll just keep reading, and then you will have marked up the page for nothing. Don't begin your critique until you've read, seen or heard the work in its entirety.
Begin with a compliment. Find something you like about whatever you're critiquing, and allow it to be the first thing the person you're critiquing sees or hears. If you're critiquing a packet of poetry, write "Beautiful imagery," or "Stunning metaphors," on the first page. If you're critiquing in person, start with, "Before I begin, I want to say how much I enjoyed your subject matter." Find a way to state what was done right before you go into what could have been done better.
Be specific. Being general when noting a critique doesn't help the person trying to improve. For example, if you're critiquing a play, don't say something like "The first act dragged." Instead, say, "The first act began with a lot of energy, but the conversation between the two lovers toward the middle took the momentum away. Perhaps the couple could argue, or walk around during their discussion? Just a thought."
Give examples, so the person being critiqued knows exactly what you're talking about and (if they choose to) can go back and change it. Rather than saying, "You had a few run-on sentences," actually read aloud or underline the sentences you're talking about.
Use supportive language. Rather than saying, "I didn't like this", or "I didn't understand your imagery," say, "I think I would have understood this characters motivation better if you had included some of his back story," or "I might have liked your imagery better if you would have compared it to something concrete."
End with a compliment. Let the person being critiqued feel as if they've done solid work that just needs a little tweaking. If their work needs a major overhaul, make them feel like its within their ability. Point out the qualities you like that you hope they'll keep.