Wholeheartedly agree with the advice given above. I prefer to treat these activities at learning/critique for the photographer and the audience. Don't take it too seriously, egos left at the door and everyone will learn something new.
I was president of a local club here for several years, and was invited to critique work for other clubs during that time. I prefer this to "judging" competitions, as I think the best reason to voice an opinion of someone else's photography is to help them improve, if possible, and to learn about another photographer's thought process. I learned a lot from looking at other people's photography and giving them an opportunity to talk about it.
1. For everyone, there are technical aspects of photography that can be learned and improved upon. I have had several prints that I was able to greatly improve after tips from several members on how to crop/compose, etc. One of those photos won a year-end competition, and it was only because I was receptive to the advice of people who I respected.
2. If you're the one doing the critique, try to understand the intent of the person who made the photo. Were they successful in conveying the message they wanted to communicate? What technical or artistic choices could have been made to make the image more successful? Sometimes photos can be all about "mood" and the technical details don't matter. If this is the case, point this out and let the photographer know whether they succeeded in doing this.
3. Make a point never to "criticize" another person's photography. Emphasize the aspects that are successful in the image and try to provide guidance on how it can be more effective to the audience, if that is what the artist is open to hearing.
4. Ultimately, anyone who wants to show their photos to another person is just trying to communicate thru photography. Many of us can't paint or write music, so this is how we express ourselves to the rest of the world. For the tech geeks, photography may also serve to satisfy other needs as well.
5. Try to leave your personal taste or subject preference out of the critique. I've seen more than one professional photographer or judge dismiss a photo because that wasn't their "type" of photography. They didn't want to comment on it because they didn't understand it or couldn't be bothered to think outside their box. No kidding, one of our invited guest judges even showed up to a meeting drunk. Good photographer - bad choices...
In-person group photo critiques are a lot of fun. I really miss participating in them, as online critiques are just not the same. I know several "novice" photographers who improved greatly over the time of just a few years. They were open to the respectful suggestions of others, and were willing to pass on that knowledge whenever they had the opportunity.