Besides some basics, such as "show, don't tell," stay in point of view, eliminate passive language and voice, and watch out for too many modifiers, I also learned the following about critique groups:
How to listen, with an open mind, knowing I can always decide not to make the particular change suggested.
What each particular critiquer brings to the table because of different backgrounds and sets of knowledge. Learn what they are, and use that person's background and knowledge to help your writing. There's the one who knows about grammar and punctuation, and is always right about that. The police officer who can make sure you've got your facts straight about procedure. The gun expert who can help you with selecting the best guns to put in your story. The good professional writer or professional editor who can make your writing stronger. And so on.
That each critiquer has a strong suit about the writing itself. One will point out the grammar errors, one will point out when you stepped out of point of view. Another will show you were it would be a good idea to put in what the character is thinking and/or feeling. Yet another will suggest you haven't nailed the setting or your transitions are weak. And so on.
Each critiquer has a weak suit. Some will insert commas that are not needed. Some will have a list of items he wants to see at the beginning of each new submission such as setting, description of characters, whether the character is male or female, and so on because he doesn't like learning later that he's wrong about any of those. The problem with this is if you do that every time, it becomes boring and most likely will slow down the story. And you might have two people disagreeing about what they want to see in the beginning.
Each group will have a set of grammar rules, for example, no semicolons in fiction. Groups often label "bad" words which can include "was," "walk" 'went" "got" all words ending in "ly" and so on. Generally, it's best to follow these "rules," but not slavishly. Sometimes it's better to use a modifier. Sometimes a "was" gets the job done the quickest and best way. And so on.
How to be a good critiquer yourself--what to look for in other people's work, and then apply it to your own so it becomes part of your tool kit for writing well.
To listen even if you don't like the person doing the critique. And not to give undo attention to someone else because you like her so much. In other words, while being critiqued, only concentrate on what the critiquer is saying, not whether you like her as a person or not. When socializing with other writers, then you can try to avoid the ones you don't like, and stick with the ones you do. But even a person you almost hate may say just the right thing to take your story from good to fabulous.
Realize that if you have to explain what you wrote, you need to fix what you wrote. If your story is published, you won't be around to sit at the reader's shoulder and explain what you meant. It has to be on the page. This doesn't mean you can't say ANYTHING about what you wrote. You are free to give background, interesting tidbits about the story that are not on the page because of number of word constraints, and so on. What this means is if readers point out that they don't understand what you wrote, especially if it's more than one person, you need to fix it, not explain it to the group or person. And in most "live" groups (as opposed to doing this on-line), you are supposed to wait to make any comments or ask any questions until everyone has finished critiquing your material.
If more than one person mentions the same problem, pay particular attention. If three or more mention something, you'd better fix it, even if you don't totally agree. There is usually a way to fix it that will make both you and everyone else happy.
Learn to separate yourself emotionally from the piece being critiqued. You MUST learn how to do this. The critiquer is not trying to put you down, he is trying to help make your piece better. (Unless he's just a jerk, but remember, even jerks have their good days.)
When the critique is over, go over all of your piece, word by word, with the critiquers' notes in front of you. I like having them all printed out including my piece. Then I staple all the pages of the critiques together page by page. In other words, all the Page Ones are stapled together, and I look at my Page One draft and make changes, line by line.
Learn to be a good critiquer yourself by watching and listening to the ones in your group who are the most listened to. Hone your own craft more quickly by noticing mistakes others make, and then not making them yourself.
As a critiquer, be kind. Some folks are quite sensitive about their writing and need a more gentle touch. Others seem to welcome a harsh critique--it gives them something to work with later.
Learn to enjoy the process. It's exhilarating getting that first draft done and ready to be read by others. But editing what you wrote is just as important. It's a four-part process, I've found. First, get that draft down and completed to the end. Second, edit it, either with others, or by yourself. Third, submit it. Fourth, when it's published, publicize it. In today's world, if you skip any of those steps, you won't get as far as you might like. So, it's best to enjoy doing it all.
What have I missed?