I think there are two types of critics. The first one is that one moron who has his top so high up his bottom that he forgets that literally no one asked for his opinion (emphasis on OPINION). I beg of you, do not be this person. I sincerely doubt anyone will enjoy your company if you're like this. The second kind of critic, who manages to help you grow and overcome your flaws, is the kind of critic you want to be. With that out of the way, I hope to be able to advise you on how to be the second guy.
If a rulebook were ever made regarding this particular topic, number one on the list of rules would be to NOT LET YOUR EMOTIONS SWAY YOU. This doesn't necessarily have to be in terms of hate only. Yes, hating on something is where people tend to get annoyingly passionate, but you'll find plenty of people who, say, listen to a piece of music that they perhaps relate to and shriek “OH MY GOD THIS IS THE BEST THING EVER MADE IF YOU DON'T AGREE WITH ME THEN YOU ARE WRONG,” like some incoherent banshee.
Really, this is just a reverse kind of hate, in a way. Remember: the person you are trying to criticise must actually take into consideration whatever you've told them. While different things do work for different people, in general, if you respond with criticism that's filled with negative vibes, the other person is likely to get defensive. Similarly, overly positive criticism might just inflate their ego to the point where they refuse to see flaws entirely. A skewed perspective does not deal out good criticism; remain calm, and you'll do a much better job at not sounding like a total snob or a yes-man.
Make sure you understand the subject involved. A painter is much less likely to be able to accurately criticise the work of a dancer. Similarly, a dancer might not be able to accurately criticise the work of a musician. This is still staying out of specifics: the three things that I mentioned are all three separate art forms entirely. Even IN the art forms, you get different styles. For example, in art, I prefer sketching and using colour pencils. If you came up to me with an acrylic painting for me to criticise, I would blatantly refuse to do so because I've literally never painted properly in my entire life before. It doesn't even have to be a creative-based subject; if you asked me if your marketing campaign is good, the only thing I'd probably be able to tell you is whether or not it's a marketing campaign. This, I think, should be something you should always keep in mind: there is absolutely no shame or direct harm done in not being able to criticise and say no to someone. You can't expect to know everything, and that's okay.
Please do give your criticism some degree of depth. If you feel like something is difficult to understand, then tell them why, and tell them how to fix it instead of just saying “I don't get it” over and over like a goldfish.
Now, this is the most important point I'll give you. Take a moment to look at the first type of critic I mentioned. Has anyone asked for his opinion? No? Okay. Has anyone asked for yours? No? Excellent! If the person hasn't asked you to criticise it, then please, put it where the Sun doesn't shine and keep quiet.
In any case, these are, I suppose, some main points to remember. There are obviously some small bits here and there, but the list is a long one. Ultimately, remember: criticism is not JUST opinion. It's this wonderful blend of opinion, advice, suggestion and the application of experience and knowledge designed to improve something. When you do it, don't pull a Shia LaBeouf and “just do it,” do it right.