If there's one thing I've done a lot of, it's critique. I've been through numerous types - from your "oil painting of flowers" discussion of composition, colour and proportions to the "Jesus in urine" conceptual bullshit critique. I've sat through some of the most horrid critiques to possibly ever have existed, and some of the most compelling, of which could have been transcribed into books on philosophy, sociology, art theory or even rhetoric.

Over the years, I've picked up several habits that have been condusive to a helpful critique. Critique is a process by which artists discuss their work, their processes and come away with an idea of what needs more work, if anything. Critique is also a method in which art audiences can deconstruct and understand art in it's socio-historic context, and in relation to their own values in aesthetics and even in a logical or philosophical framework. Artists receive a lot of critique, but audiences tend to lack in their ability to work through critique, as the method (a systematic inquiry into the conditions and consequences of a concept or set of concepts) is not often taught in basic education and is downright discouraged in everyday interaction in our consumer driven society. If one were to engage in critique in every aspect of their life, they would question the decision to buy, and has, so far, been the adverse of what consumption is going for.

Thus, many audience members tend to fall back on simple comments that we're used to in everyday interaction, like, "it's beautiful!" or "I love it", which is astoundingly frusterating for artists who are trying to engage beyond the aesthetic level of their work.
Before I move on to the actual tips, I must give a short, but relevant disclaimer. The bulk of my studio critique training is with highly conceptual art. Square cube in the middle of the floor type conceptual. Thus, my qualification for a "successful" critique is one that delves deeper than a denotative description, or disagreement. Comments like "the anatomy is wrong" is not helpful in this sense, because it is a superficial critique. We have the goal of getting "into" the work, not just simple looking upon it.

Without further adieu, I present the Deviant Art community with my comprehensible and concise tips for a successful critique:

1. Spend time with the work you will be critiquing. You cannot expect to give a good critique if you spend thirty seconds with a piece and then jot down whatever comes to your mind first. The artist has most likely put a good deal of time into the concept, planning and execution of their work and is looking for someone who will spend a decent amount of time "reading" their art. Now, the methods of doing this differ wildly depending on who you talk to. Visual Culture critics will read art differently than classically trained sculptors. I will give you my method as an example, but it's important for you to develop one that works for you!

In reading a piece, I often read it, at first, like I would literature. I start at the top left and work my way down to the bottom right. After that, I allow my eyes to wander on the picture plane and rest on the focal point of the image. Then I will give myself a "denotative" description. Denotative means descriptive, those things that are... take this [link] for example. A denotative description would include the following:

"There is a girl, dressed, sitting on the grass. The camera angle is from above and she is looking up at me."

I will follow this with a connotative description. Connotative is a little more complicated, it's what we understand from the codes in the image. These are highly cultural understandings and will differ from person to person, and especially country to country. My particular connotative description may go as following:

"The girl is young looking, yet she is dressed up in mature fashion. It comes from the codes of fashion photography, and she is subjected to sexualization not only by her manner of dress, but also the angle from which we look down on her. We are the dominant viewer, and she is being viewed, we are positioned as dominant, if not her direct superior. She is looking directly at us, but not in a defiant way that would attempt to recapture some agency like in Manet's "Olympia", rather she is acknowledging and almost validating our presence and power over her."

At this point, I would find something interesting within my connotative description that I would want to share with the artist. If I haven't come up with anything that I feel in interesting, I don't say anything, which leads in to number 2...

2. Silence is golden. This is simple, if you don't have anything interesting to say, don't say it. Critique is not supposed to be negative or positive, it just is. "I like it" is not a critique, and subsequently "I don't like it" is also not a critique. If you simply like it, then say so with your and leave the space (and comment reading time) to individuals who will give critique. If you feel a certain way, such as liking, disliking, offence, etc, that's for you to figure out, not the artist.

3. Assume that everything is intentional. If you go from piece to piece pointing out the flaws, this is most likely not useful to an artist. I find this is the most frusterating in my work because my "flaws" (in anatomy, composition, technique and the like) are often intentional, and are meant to go with the concept of the work. Go through your denotative and connotative descriptions and present your results assuming that every aspect of the work is meant to be like that. If the eyes on a particular drawing are too far apart, put that into your denotative and apply it to any concept that might come out in the connotative. If the artist didn't intend for the eyes to be wrong, they will pick it up in your critique of their concept, because their intention and your reading will not match up.

This is a very important part of critique, because an artist doesn't have the luxury of explaining themselves through the concept of their work. They can't be with every viewer at every minute explaining in words why they did what they did. The concept has to be made clear by, surprise surprise, their ART! My connotative description of the picture above may not be what the artist was intending, but that's irrelevant. The connotation is what's in the visual, and can not be garnered by some psychic power from the artist's brain.

If the artist of the photograph I critique did not intend to be so subjugated, perhaps she will redo the picture with a different angle and method of dress, thus my critique was successful in helping them understand how an audience will read the work.

4. Enjoy getting into discussions on your critique. Any artist that takes offense to the time you've spent in putting together a critique for them is not worth it, spend your time with someone who will appreciate it. However, don't mistake discussion for dissent, often artists ask for clarification or for you to delve further into your analysis. Be prepared to do this, and don't add anything to your connotative description that you can't continue on with (within reason of course, you shouldn't be expected to write a book to justify your position).

5. Practice critique as often as possible, even if you don't leave a comment. As with most things in life, and as with art itself, practice makes perfect. You can't expect to be the best critic overnight, it takes practice, patience and a willingness to fail. Along with your practice, get into art history, philosophy, sociology and theory on critique itself. If you're really interesting in this practice beyond the scope of Deviant Art, it's important to be well read and open to all sorts of opinions.

I'm sure there is more to say on this interesting subject, but I think this should do for now. Feel free to ask any questions, or even give critique on my tips for critique. There's nothing I love more than a good discussion!