I remember being a young boy of 9 and being hauled out of a swimming pool for mouthing off to a coach at a team tryout. It was a pretty dumb thing to do and the coach gave me something she called "constructive criticism". Constructive criticism is when someone criticizes what you have done, and then offers advice for doing it better. Indeed, that day she gave me some constructive criticism about how to respond to constructive criticism, which was to take it with good grace, because the critic was offering it in good faith.
Often times criticism is taken to be mere insult, and I believe that is because it is neither offered well, nor understood upon receipt. I've been on both sides of the equation, and I expect most people over a certain age, say 12, have been. Now, as part of my re-training as a technical writer part of my editing courses were dedicated to editing nicely, because when you're not nice the people you're critiquing tune you out.
However, there are some things that cannot be said nicely, and contrary to what some of your mothers may have advised, they still have to be said. Constructive criticism doesn't have to be nice, it just helps. For people with a thicker skin, or those who are used to being critiqued and who are looking for advice, sugar-coating it won't help. That's not to say being rude does anything but make the advice-giver look like an idiot, but that people respond better if they are interested in internalizing the critique rather than defending themselves from it.
Just about the worst thing you can do when offering constructive criticism is argue, which is in part why I prefer the blog format to the message board format: message boards invite a competitive-debate style environment of scoring points rather than the transmission of information. That is because no-one will take advice that they do not want. Quite simply you can never change another person's opinion by argument unless they want to change their opinion.
That's why I try (and often fail) to adopt a formal tone, in the hope that my readers will clue in and realize I'm trying to talk objectively rather than soft-pedal a point as 'my opinion'. In constructive criticism you state the goal, the problem reaching that goal, and how to overcome that problem. Of course, you can be wrong ("That's just, like, your opinion, man!"), but that's not a problem of subjectivity as a problem of error (which is impossible if the truth-value of the opinion is entirely subjective).
There you go, constructive criticism should be simple: State the goal, the problem, and the solution. If you just state the goal, however, you're implying someone is too stupid to reach that goal. If you just state the problem then it just sounds like you're trying to insult someone. If you provide a detailed and careful statement of a solution, to someone who's seeking your advice, then you just might succeed in a critique.
It's also worth noting that intelligence is divorced from intellectual tools. There have been plenty of geniuses in the history of the world that were unable to realize their genius thanks to the tools that were available to them, their genius being recognizable through the methods they developed in the absence of those tools. Sometimes, no matter how you can phrase your critique, and no matter how smart the recipient is, your advice will fail to be taken up because you're not using intellectual tools that they share.
There's virtually no way of avoiding this last problem, particularly since the use of intellectual tools must be trained into someone as well as learned, but sometimes the good will is enough that the critiqued might at least find motivation to acquire these tools. But the unfortunate fact is that most adults are incurious creatures content in their own ideas, and proud of what they think they know. I was a child when I learned of constructive criticism, and had an interest in accepting advice (the interest being: not getting kicked out of the try-out!). Not everyone has that motivation.
So, to re-iterate: Constructive criticism works when it is offered correctly (goal, problem, solution), understood, and in the context of motivation to apply it. Otherwise, well, you can bother but it's really just catharsis.