I could write a book on critique, which turns into edits when it's my own work.
But the place to start depends on what your weaknesses as a writer are.
I urge you to jump in at the SYW board for any genre you read, even if you don't write it. Find something fairly recent, so you're not zombifying a post, and read it through. (Stop at the end. Do not read any other critiques.) What works? Do you like the title, tone, style, character descriptions, mood, setting, plot, vocabulary, vibe, etc.? Great, tell the author and use examples. We all need to know what we're good at.
What doesn't work? Tell the author with kindness and tact, explaining what your issue is, and use examples. We're not talking errors but weaknesses. Step back for the big picture. Was the character a trope, or too something to be believable? Is the plot stale with nothing new to add? Is there so little description that it's set in a white box rather than a place you can envision? Does the author tell us too much about characters' appearances down to their clothes and hair? Is there a coincidence you can't swallow that's vital for the plot to progress? Does the author tend to reiterate, use state-of-being verbs rather than something more lively, get downright wordy, insert his or her opinions, etc?
And last, does the work contain mistakes? Fix them, using a contrasting color. Oh, and while it's tempting, resist the urge to rewrite it the way you'd write it if it were yours, because guess what! It's not.
Maryn, who got better at critiques by doing several hundred