Doing a critique for a writer is much like being a beta-tester for software, which is why the term "beta-reader" is commonly used. Once the author has finished rough draft, first draft, then final draft, it's time either screw in a fresh set of eyes and re-read it again (which many authors can do), or to let someone else read it.
A critique is more than just a response e.mail saying, "It was great! Keep up the good work!" Your work could be lousy, and a polite friend would congratulate you on your efforts. If it truly stinks, they may just remain silent. If you persist in asking your beta-readers to read really crappy stuff, they will start to refuse sooner rather than later.
So what is a good critique? It's feedback that lets you know what worked and what didn't. You might have great characters, but a lousy plot. A good critique will give you that information. If you CONSISTENTLY have good characters but lousy plots, then that gives you a clear indication of your strengths. (It also gives you something to weep in terror about about late at night as you contemplate yet another rejection from yet another editor who probably demands good plotting above all else, but that's another issue.)
Writer's workshops offer critiques as a selling point. The people in the workshop/writing group/class/etc. are not your friends, and so have no social capital invested in their relationship with you. They will be honest. The truth hurts, but if you don't know what's wrong, you'll never be able to fix it.
Theoretically, a friend will be honest too, but don't push it.
Experienced critics will know what to look for. This is a set of general critique questions developed by MarFisk, posted on the Forward Motion website. A variation appears here. This is not necessarily a checklist-type activity, but these are the things to look for.
Plot elements (in each chapter, things to be developed which are central to the plot and/or subplots):
What I liked in the story:
What I didn't like in the story:
A link to the story of mine I would like comments on: (if applicable)
Notice that last item. Critiques are like anything else... if you want it, you should only ask for it if you are willing to return the favor.