There is a huge part of making art that consists on improving your art. And one way of improving your art skills and understanding is through critique people would give you. This article is about understanding the notion of critique in order to make it the most efficient possible for you and for everyone.
Everything you will find here was probably said a hundred times before. But I am sure that many of us still are trying to find the right pattern to follow in terms of critique, and it isn't easy.
Let's start with....

...Wow, awesome!

At some point we all have to deal with the "wow, awesome!" comments. "wow, awesome!" is not a critique. It is a form of feedback, communication, self-expression, - a way to tell the world "I like this piece, and I want you to know it, I want the artist to be informed, I want to leave my word on this piece." Don't underestimate the power of "wow, awesome!" though, it is definitely not pointless and not to be considered as spam nor ignored. It might be by far more encouraging for the artist then any other form of feedback, it contributes to the overall community spirit and is - a pretty basic - but still really positive way to share art and our feelings about it. But "wow, awesome!" has nothing to do with critique.

Critique

There's something mean, almost terrifying about the word critique, it feels like it was made as a scary punishment for the naughty artists that mess with their work. Critique doesn't have a one-way all-negative meaning we sometimes see in it, it is a form of feedback that aims evaluation of art, on one hand, and help, on another.
Critique is an art on it's own.

The Dos and Don'ts

Do feel free to like the piece of art you want to review. You don't need to hate the picture to give it criticism. And since you like it, then do try to find and point out why. If the artist is good at something, (s)he would probably want to know it at first place. And it might be interesting for you as well to analyze what exactly makes you like this certain picture. The results of this analysis may be not as straight forward as it sounds.

Before you say anything, do make sure you make the difference between what you personally like/dislike in an artwork, and what really is/isn't good in it. Make sure you let the artist know as well. Your personal opinion about the picture is, certainly, to be shared, and is, for sure, interesting for the artist, but there are certain points in your feedback that should be as objective as possible. So please separate those two as clearly as you can.

Don't rush. Sit back and think if what you are going to say is what the artist really needs to know, or is it just your personal issues that make their coming-out. Seriously. Critique isn't something that is supposed to make you feel better. Isn't something to make you seem cooler within the community. It's not showing off that you can draw better - this you can do by actually drawing, right? So ask yourself why are you giving feedback - sit back, - and if you don't feel that you would want this kind of critique, then let it go, drop it, and move on to something else.

Don't plain simply and uselessly hurt the artist. Of course you can be very straight forward about something that is wrong, you don't need to be over-polite and gentle and only talk about the good aspects of an artwork in order to spare the ppor artist's feelings, this is not the point. But if you somehow feel like everything is so wrong, and so flawed, and how come the author doesn't even see it?! - be sure that telling this wouldn't help a thing. If everything is so bad, and the artist can not see it, the best you can do is to encourage him/her to work further, and let time work it's ways. Eventually, only with work and practice the artist would end up seeing what you can see on the picture.
What you should keep in mind, is : eyes always prevail. You can learn anatomy by heart, every bit of it, but if your eyes don't see and your mind doesn't have the intuition of making the link between the picture you draw and what you know - critique won't help. The best you can do as the critic, is make the artist want to work further on, - and how to do it, is up to you

Do point out the flaws.
But you don't have to make the whole list of them, if there are plenty. Pick what you think is the most important - for the picture and the artist to work on - and insist on it. But do insist if it is worth it!
make sure, though, you don't say exactly the same thing as the person above you. A repetitive negative critique is not much of an encouragement.
Do provide solutions that would fix the flaws you have pointed out. Now that the artist sees what is wrong - make sure (s)he can learn how to make it right, that's the most important of all things! that's why we want critique, that is why you are needed.

Do avoid the use of subjective "I would draw it this way.." and "I would rather..." What is important, is not how you would do it, but how it should be done. those two may be much of a same thing, but the artist doesn't know it, and (s)he might find it offensive that you project yourself on his/her picture. Most of the critique's art is a matter of how you say it, not what exactly you say.

Do feel free to justify your critique, especially the negative one. Not that you need to justify yourself in order to make people believe what you say, but if you let the artist understand your point, be sure (s)he will dig it, and your work will definitely be worthy.
And for this, do make use of images/photos/quick drawings/overpaints/ red lines to make your point clear. As far as the graphic arts are concerned - an image is far better then a hundred words. But if you want to make it clear - you'll probably need both: pictures and words. Get a stock photo, google the matter in order to find an example - if the artists is receptive and longs for an explanation, take 5 minutes for it, and I am sure you should feel like you did the right thing.

Critique is a complex craft, but if you do it right, you will surely make friends among the art community and, probably, set even your own self on the way of improvement. Every time you write a critique is like looking back to the progress you yourself made in drawing and understanding art, in skill and ability to see what is right and wrong.
In fact, unlike what I previously said, critique is a little about yourself too!
So enjoy it, and be true.

Accepting critique
Accepting critique is actually as hard as writing it. Accepting and thinking it over, paying attention and making a list of good resolutions to hold on to. It is hard, I bet you know something about it.

Don't believe that the secret of you improving your art is critique. Good critique is a rather of a helpful thing, but once you got it (if you get it) it's up to you what to do with it. And now the hard part starts.
And now it's up to you.
Do think the feedback you got over. Carefully. Make sure that your esteem of your art doesn't get hurt by anything that you read. Make sure your esteem of yourself isn't to high for you to allow you to read critique as well. If you don't feel like you can handle it, well, don't. Ignore a couple of comment, it ain't a big deal. or tell people you don't really want critique for the moment.
But if you're ready for it, go ahead and have a first read, to get the general mod and message that the person wanted to send. You have the right to reject a non-constructive, non-tolerant, bad-mooded, or simply mean review. You don't need to care about everything everyone says!

You do have the right to disagree with a critique, even if it is well-done, constructive and justified - if you do, make sure you have good reasons not to. You may want to tell it as well, and explain, justify your point. May be you will be proved wrong. Or perhaps the critique him/herself will learn something interesting from it! Do share your experience.

An important point. Don't judge the critique. A critique doesn't have to be a master of art in order to give you reasonable feedback. Of course if you find yourself reading a review written by a 10-year-old who's main point is "wanna qraw qnime, lol!!1111" you may not want to take his/her opinion too seriously. But a good critique isn't necessarily someone who draws well. So don't base your opinion about the review completely on that person's art skills.

if you feel that the review deserves attention, - and it certainly does if the person took time to analyze your work and put it into consistent words - then do take some time to read it more carefully, compare with what you think about your artwork, and how you see it. You should probably find a couple of things you may agree, at least partly with, after a certain thinking through it. And if you do - you're on the right way on to improvement!

If you take a careful look, with some distance and time you always find flaws and glitches in your work. Critique is here to accelerate the process.

Now, once you know there are some points you should work on in the picture - all you have to do is to work out how. Don't be afraid or ashamed harass the people who critique you, in order to get an idea bout how to deal with what doesn't work in your art.

Do be ready to hear the following things:

- "Goole it". Tough. Rude. But true. You will have to be searching for the resources you need for your improvement yourself. You have the right to feel angry at the person who says tis to you. But eventually, if you end up googling (or something else) what you need, then, after all, it was the right thing for you to hear.

- "Would use more work". Not really gentle, right? probably true. But not really encouraging. Try to take it as an encouragement and just keep on working the way you did - with time and sweat you will make it.

- "I don't know why, but this just doesn't look/feel right". This is particularly nonconstructive. But I am sure you yourself sometimes get this sort of feeling of "wrongness" in a picture without being able to tell why. may be because you're not good enough of a critique. Try to go back to your picture from time to time and wonder if you yourself don't see that somethings wrong.
If you don't, then may be it was just the wrong thing to tell.Or you need more time.
If you do, then you are getting better. Or you were a little bit careless while drawing your picture - this happens, there's nothing wrong with it as long as you are able to deal with it.

Do enjoy compliments. Any kind of compliments. And once you have enjoyed them you can also try to analyze them and see what people really like in your artwork. To keep it up. And please, in any case, DO keep your art up!

Thank you for reading!
I hope you would have found it helpful, interesting or at least entertaining. I hope you will happen to think it over while writing a comment next time, and put more of yourself in your writing feedback, and your reading it.