I think its good to find a balance between helping with some cleaning (if they'll let you) and doing some reading or looking at interesting things. While cleaning all the time sounds like a way to win people over, it may just make them feel awkward because, A, it kinda sorta is illegal in many circumstances, and B, they know that you're there because you want to learn, not to scrub counters. Looking at records is fun, and it's useful to become familiar with terminology and abbreviations, and I would also sometimes pull out the drug formularly and read about drugs we prescribed a lot... or more often for me, whatever drug we had just put my poor bird on... My favorite thing to do was looking at rads. I would also sometimes bring in a fecal from my bird and spend some time exploring all the fun things she had hanging out in her poop... and even diagnosed her with clostridium infections a few times. You will never ever run out of things to look at/read in the average vet clinic, as long as you know where to look... or ask.
But whatever you do, I would not advise sitting around on your phone or reading a non-vet book, or just looking bored. If you're going to do that, you might as well leave. Personally, it would annoy me (and our hospital manager) when my fellow interns would use their down time to study for an upcoming exam, but then again, I was out of school at that point, so maybe I would have felt differently in their shoes. I think in a volunteer or shadow setting, if it's so slow that you actually have enough solid chunks of down time to study, you're better off just saying, "hey, I have an exam tomorrow, do you mind if I head out since things are slow?"