At my first writers meeting, I received a handout on a very useful template on how to critique someones work. Now granted, I personally haven't used this exact structure in my own critiques (I prefer to give verbal feedback because I still don't feel I'm at the level to write on someone's manuscript), but it's very useful tool for giving effective critique. When I receive critiques of my own work with these points addressed it's incredibly helpful:
1. A Summary of the story in a few sentences.
2. What are the Strengths of the Story?
3. What are the Weaknesses?
4. Suggestions for improvement.
This format is very useful because it highlights what you did well, since no one likes only negative criticism - even when it's constructive, but it also highlights one's strengths. This is good for morale, but also helps to gauge what I'm good at and it helps me to develop my positive traits and become self aware of my writing. Knowing the weaknesses of course are a necessarily evil. There is always going to be something wrong, something that seems awkward, insecure, a continuity error in the story or even just the grammar. We need our weaknesses pointed out so we can actually do something about it. It doesn't need to be disheartening, we all make mistakes - especially a novice writer. We are not born great writers even those with great talent work their butts off writing everyday and learning from mistakes; writing is a craft which needs to be worked on continuously.
My confidence has increased on the criticism front. I know a lot more about writing from my own mistakes and having read a lot of books about writing. The hours spent on redrafts and re-writes I have made on my own work has taught me to be critical, initially with my own work and now I can apply that same critical eye to the writing of others.
One doesn't need to be an expert to give criticism. This is a very important point I learned. We buy books, read magazine articles and recite poetry (ok the latter not so much...you'll find me reciting Monty Python or Black Books before poetry) and you don't have to be an expert writer to know what you like and dislike and what doesn't work. We all have opinions, sometimes that is all one needs to exercise. It's nice getting feedback from someone who knows what they are talking about, but every opinion is valid so why shouldn't your own be?
Giving your own opinion and criticisms not only helps other writers, but also helps you. It teaches you to develop the critical eye you'll need for your own work and gets you actively thinking about the strengths and weaknesses of other writers, who wont write like you do (none of us write like each other - that's the beauty!).
I think it's important to remember though that another writer's style is not yours. This is a point one also needs to bear in mind. When someone sends you their manuscript, unless they're asking you to ghost write, for heaven's sake don't bloody rewrite it! I know it's tempting to put things in your own voice; I'll look at a sentence and think "hmmm I would have written that differently" and there is nothing wrong with the suggestion, but often there needs to be the ability to distinguish what is general criticism, something which is a universal weakness to a personal preference. It's good to be clear on these things as you are sure to see different people giving different pieces of advice. Your opinion matters and could indeed be useful, but it is subjective.
Critique the work of others and you'll be able to look at your own work objectively as well.