Do
Talk about the design in the context of your project's goals. You might say something like, "I like how the navigation gives the user a clear path to follow." Or if you don't like something, "The imagery is setting the wrong tone. I want to emphasize the diversity of our offering rather than focusing on one aspect of it." This suggests that you are keeping the driving strategy of the project at the front of your mind.
Give both positive and negative feedback, preferably back to back. Bear in mind that only giving negative feedback gives the impression that the project isn't going well. By including what you do appreciate, it allows the designer to understand your preferences and to build on those in future iterations. (It's also just a nice thing to do. A happy designer is a helpful one.)
Identify the trouble spots as they impact usability. Hopefully, the designer will be able to craft a perfectly usable interface, but you know the quirks of your own target audience. If something's going to prove difficult or confusing, or if it doesn't have the desired effect, be sure to point it out.
Remember your end-user. Sometimes we get so caught up in making a site or app that appeals to ourselves that we forget who it's really for. The designer should help you stay on track, but remember your end-user when you give feedback. Think "Will this feedback benefit them?"
Don't
Don't feel like you have to come up with solutions to every problem. As long as we know what your goals are, and what matters, we can create those solutions for you. That's the value of a professional web team.
Don't give conflicting feedback. Use the existing design to help you zero-in on your intended direction.
Don't ask everyone you know for feedback. Chances are, the project has an intended audience. Those are the people we care about the most, and who we're trying to optimize the site or app for. Your brother’s kids? Probably not. Trust your designer, trust your audience, and trust yourself.
Don't project your own personal issues and associations into the design. This happens a lot during large design presentations, when one person will make a stray observation that gets the whole room nodding. Something to the effect of "That color reminds me of (blank)," or "The guy in that picture looks like (blank)." Let's stay focused, and remember what’s important. And speaking of focus…
Don't get distracted by placeholder content. The difference between print and web design is that the web is dynamic. It changes. So if a header doesn't read properly, just confirm that it’s editable in the CMS and move on.
Don't feel pressured to give all your feedback right away. First impressions are telling, but it's good to take time to think things through, and see how the design looks after letting it rest.
Remember that feedback works best as a conversation rather than as a list of changes. Often times, solutions come out of thoughtful and thorough discussion. Be open, be honest, and try to be nice.