The most important thing about giving someone a crit is that you should always be kind instead of nice. A nice crit is telling someone their work is pretty good just to avoid hurting their feelings. A kind crit is telling someone their work is not where it needs to be so they know it needs to be improved or refined. Be kind and honest, instead of nice and disingenuous. Also make sure that your feedback is not derogatory, insulting, or dismissive of the person in front of you. Remember that giving a good crit has absolutely nothing to do with being mean.
Generally you should try to avoid giving corrective critiques — comments like “I would do it like this” or “you should try it like that.” The work is not about how someone else would do it, it’s about how you would do it. The main problem with corrective crits is they often lead to a direct duplication of that comment — and that is not the point of critique.
While there is a bit more relevance in corrective critique for entry-level students who are learning the fundamentals of their profession, it should be done sparingly. The catch is that it is very, very easy for students to develop a habit of relying on crits to tell them exactly what to do next, rather than developing their own exploratory process. A lot of art and design education is about trying stuff until you figure out what works — being prescribed the exact “right” answer does not let this happen.
If you are not sure what to tell someone who is asking you for feedback, a good place to start is by simply describing what you see. Telling the creator of the work what you are seeing can be very useful; for in-progress work, it is often different from what they intended to show you. Telling them what you think they are trying to say will help them understand what the work is actually saying.
Another good place to start is by telling the person getting the crit how the work makes you feel. When you look at the work, do you feel excited? Confused? Bored? Angry? Calm? Happy? Sad? Regardless of whether the piece is “art” or “design,” your emotional response to it is valid feedback, and can help the creator of the work create something more meaningful.