My advice, which comes a quarter of the way through my second REU with the same lab group:
The professor you are working for is probably one of the most knowledgeable people in his field that you have ever met. Thus, don't try to pretend you know more than you do. He/she will be able to tell when you do this. Your adviser is going to know more than you, but the good thing is, unless he/ she is living in some ridiculous bubble, they will not expect you to be as knowledgeable as themselves or their grad students. He will know that you are there to learn. So, here is how you impress:
1.Be willing to learn and don't back down from any task they give you. (If they are asking you to do it they must be confident that you can handle it.)
2.Work hard. Even when I don't have anything pertinent to do during the time I am working, I am still in the lab. I either read research papers or practice GRE problems. If they see that you are always driven to do work and get things done, they will definitely be impressed. If you feel you would like more work, ask! here is always more work to be done in a science lab. This year, I am getting to work with much more sensitive and expensive equipment so this advice must have some merit.
3.Accept that you are going to screw up and be open to any advice you get. The people you are working for are going to expect you to screw up. What matters is how you take it. If you accept that you will screw up and focus on learning and not making the same mistakes over again, you will make a good impression.
4. Be openly interested in what's going on. Chat about the research with grad students and your adviser when you can. Read the group's old papers. Do everything to show that you are serious about making as much of a contribution that you can.
5.Learn something new! If you can accomplish this point, then your REU was a success.
As far as I can tell, and I'm sure those members who have advised REU students will agree, the REU is what you make it to be. It can be 10 weeks where you are in a lab and you do some odd tasks here and there and get out of work as soon as the whistle blows. Or, it could be something where you take 10 weeks to make connection, learn new material and useful skills, and maybe contribute enough to gain a publication.