There are different approaches of critique for different skill levels too. Beginning artists can be easily crushed and strangely enough, so can the very experienced. I think this is because both ends of the spectrum get a lot of kudos from family and friends (and customers and other artists at the other end) and may not be ready to hear that things still need work.
So, for a beginner you want to be gentle. Usually the issues are basic. I usually start out with what is done well, praise and encouragement go a long way. Then it helps to give some direction for them to work towards. Simple things like aligning all the features of the face, or doing hair in blocks of light and dark instead of strands. Or how things in the distance cool, so blues are more effective for distant mountains. You also don't want to overload a beginner and overwhelm them, so pick just a couple major things and give them ways to work on it next time. And I usually do say 'in the next piece' because overworking something can make it worse.
The more experienced artists are going to have more illusive things disturbing the flow...perhaps the light source is off in a certain area, or you don't quite get what the focal area is. Sometimes the work overall is so good that just one little angle being off can stand out like a sore thumb.
The point of a critique is not so much to be critical as it is to give the artist information that will be helpful to them. It should be done in a humble (no one likes a know it all) kind way. Kudos will help no one grow.
The way I think of critiques is that it's like being a mentor. I truly want this person to grow because I see potential and I have the knowledge that will help them. I got this knowledge not just from experience (the best teacher) but also from people who were willing to share their knowledge with me. It's a pass it forward thing, so if you think of it that way then it will come easier.