It's only natural to want people to like our paintings, but if we're to grow as artists, then we need statements that say a little more than simply "It's nice" or "I love it" or "I don't think this painting works". We need information on what specifically is nice, loved, or isn't working. Specific, constructive comments will help not only the artist whose painting it is, but also other artists reading the critique. It will also help you look at your own work with a fresh eye.
But I don't know much about art or painting, so I'm not qualified to critique
You don't need to be a professional painter commanding high prices for your work or have a degree in art history in order to critique a painting. We all have opinions and are entitled to express them. Think about what you like or dislike in the painting, focus in on why you like or dislike this and then put your reasons into everyday words. Is there anything you think could be improved or would have done differently? Is there something you wish you'd thought of doing? Don't feel you need to comment on the whole painting; even a sentence or two on a small element will be helpful to the artist.
I'm afraid I'll hurt the artist's feelings
Any artist asking for a critique takes the risk that they may not like what people say. But it's a risk worth taking to develop as an artist – and as with any opinion or advice, they're free to accept or reject it. Don't be personal; you're talking about one specific painting, not the artist. Think about how you'd feel if someone said it to you and, if necessary, rephrase it. But rather say something short than nothing; if an artist's taken the step of putting a painting out for critique, it's very disheartening to be met by silence. For me the key to critique is compassion ... show some compassion towards the artist's efforts, even if you don't think it's successful.
Technical "correctness" such as accurate perspective and proportions, is only one aspect of a painting that you can comment on. Don't forget the subject matter and the emotional impact; talk about how the painting made you feel, your immediate response to it, what is it in the painting that generated an emotional response? Look at the composition and elements in the painting: does it draw your eye in, does it tell a story that keeps you looking, where is the main focus of the painting? Would you change anything, and why? Is there any aspect you particularly admire, and why? Does any aspect need further work? Could an idea be developed further? Read the artist's statement, if there is one, then consider whether the artist has achieved their stated aim.
See also: Critique Checklist.