While it is important to understand how to receive a critique it is just as important to know how to give one. Why? Because it gives you an important perspective on how other people can and will talk about your own work. Participating in critique sessions can be overwhelming, and in the beginning it may feel dumb or irrelevant, but you should know that while you will certainly benefit your fellow artist by talking about their art, it also benefits you by allowing you to open up about talking about art in general. If you can become comfortable about talking about someone else's art then it's only a small step to becoming comfortable about talking about your own artwork, and while some may believe that their artwork speaks for itself, I'll be the first to say that assumption is dangerous and ignorant because it most certainly doesn't and in most cases shouldn't.
So open up, get comfortable, and start talking art so you and your fellow artists can get a lot of practice because if you want to keep food on your plates and a roof over your head you're going to have to do a lot of talking!
LOOK at the artwork. What do you see? Take mental notes of specific technical choices because those choices need to be addressed.
Examples: color choice, theme if any, line quality if relevant, images used, placement, proximity, everything under the sun. Composition is built by all of these technical terms and processes and by bringing them up you're bringing practicing an open dialogue with the artist that you should be having with yourself while doing your own work. What will people ask? Can you back up the answers?
LISTEN to the artist. Did they address any of their technical choices? If so, were their reasonings appropriate, or relevant? This is the part that can become personal, even though it really shouldn't be, but it's all about the delivery of the communication that can help the person being critiqued not feel attacked. Take note of key phrases they may have stated that worked proficiently or negatively toward what they were saying. Give them the initial chance to answer all of your unspoken questions.
TALK to the artist. This takes careful planning and it starts with a combination of the first two steps. To avoid confrontation be polite. I've always found asking detailed questions before telling them what I thought allows the other person to hear themselves first and also allows them to start questioning their own decisions before shocking them with a positive or negative feedback.
Ask questions that weren't answered in the initial statement, starting with certain technical decisions they made. After establishing that dialogue, start asking about the person's conceptual aspect. Why did they chose their concept, or if it was an assignment ask them what kind of research they did to plan for their final piece. Some people don't realize that artwork requires a considerable amount of research and understanding of what they're creating. Understand what you're creating from all aspects, artists are scientists too!
Now it's time to break the news on your personal opinion.
In some cases your idea was sueded by a person's explanation, and that's great! Let them know of that process, it can build confidence in their ability to sell their idea. It also goes to show you personally that when words are delivered the correct way then your personal agenda within your artwork can become clear and successful, but the wrong wording can lose an audience completely.
I would also butter up the artist by stating all of the applicable techniques that you noticed, let them know precisely what you saw. Show them that you noticed the tiny details that they put in or you could see that they spent a lot of care on a specific aspect and that it was working well. This allows the artist to trust what you're saying and trust that you want their piece to work and you're trying to understand where they're coming front.
Once you've begun a comfortable dialogue and they're talking back in conversation, it's safe to start in with what you found to not be working so much. Don't just say "this sucks," or "that's not good," either; you need to state clearly the specific choice they made, what it portrayed to you, and why you think it wasn't successful in a particular piece.
For example: "I noticed you used the color red frequently in your piece. I personally think that it was redundant in portraying the emotion you're trying to portray. It would make the piece more interesting if you didn't spell out the metaphors so clearly. Did you try using other colors in your sketches?"
In this example I made a personal statement about a decision an artist may have made. I thought something wasn't working and I felt like the piece would have been stronger if it had been different, but I also opened up to the artist to allow them to explain themselves because the truth be told, that may have been a sore point in the piece. They may have spent hours trying to make that particular decision and came to the conclusion that it needed that much red. So now they can explain to me why they fought with that decision. If they disagree, don't push it farther, you've said your peace, but if they agreed continue to discuss it with them but let them lead the discussion. Let them ask the questions. This allows for a non confrontational environment.
As a rule of thumb, I try to clump my disagreements together and get them out of the way and candy coat it at the end with a statement on how the piece as a whole may be working in some degree.
That's my personal way of doing things and it worked, nobody hated me, but you'll find your own way of communicating!
Another good suggestion on picking out parts of work that are successful is to see a large piece in parts. What is working? If you cropped the image to find the most successful aspect, where would you crop it and why? Show this to them. I had a teacher who would take a few pieces of paper and square off places in our drawings that were working as a full composition within the whole. I personally loved it and it allowed me to see my own artwork in that manner.
The best way to talk about your own artwork is to talk about someone else's over and over. As artists we are inspired by a specific sense whether that's audio, visual, or tactile and we work hard to make effective forms of communication within those senses. We must strive to look at everyone's artwork critically and our own artwork doubly so. Why? Because it allows us to dissect decisions and understand methodology so we can learn those decisions and incorporate them into our own work, to propel ourselves forward so we can create interesting pieces for ourselves and others.