All good advice so far, I'll chime in with how I expect my med students to excel:
I don't really like how the onus is placed on the student to be proactive and involved in what's going on day-to-day. Sometimes the intern doesn't even know, so how can you expect the student to know? I feel like as residents we need to be better in actively including the student in the day-to-day, including the boring stuff like making the list and returning floor pages. Especially on surgical services, it's nice to be in the OR all day as a student but you don't necessarily learn much about that particular specialty unless you see the medical management outside of the OR.
So, as a med student on clerkships, the best thing you can do to stand out is just flat out ask your intern to walk you through a typical day with them. If at all possible (which, if you're on a surgical service, can be difficult at times especially if the clerkship director doesn't want you doing that) I would highly recommend shadowing the intern for the first day so you can see what it is they do and identify areas you can help out in the coming weeks.
For example, ask to hold the pager for a day. I disagree with the general idea (or what was the idea at my training institutions) that med students can learn nothing from returning "nonsense" pages from the floor. Those pages only become nonsense when you're at a point in your training where the question being asked is elementary and you can arrive at the answer in a snap. To a student, there's no such thing as a nonsense page because they're not at a point in their training where they can instantly solve the simplest floor management problem. So when you hold the pager and have to be the one to talk to the nurse, you're already training up your clinical acumen (and of course if it's a question you don't think you can arrive to the answer to on your own, the intern is always a desk or text away).
Another thing I try to get my students to do that is relevant to clinical learning is running the list. Typically you run the the list twice a day: once after rounds in the morning and then again in the afternoon before PM sign out. The AM running of the list is where you make sure orders are put in and consults are called and the night/afternoon running of the list is where you see if what you wanted done that day was actually done. I like when students participate in the running of the list for two reasons: it shows me if they were paying attention on rounds (I'm happy if they can give me all the consults and orders for their 2-3 patients that they carry, ecstatic if they can do that for every patient on the list) and it shows that the student is trying to assume more responsibility, especially if they're writing down stuff for every patient. Running the list is also the perfect time to do some on-the-fly learning, especially if you don't know why a consult is being called or why an order is being put in for X test or Y therapy. Honestly, list running is where you'll learn the bulk of your clinical knowledge.
One more tip before this becomes a novel: if you're on a service that's not terribly busy or you're not in the OR that day, it would help the intern out immensely if you periodically rounded on the patients on your own (one of my most favorite chiefs said that his workflow as an intern was: AM rounds --> consults --> orders --> notes --> mid-morning nurse rounds --> lunch/finish notes --> early PM nurse rounds --> +/- PM chief rounds). I don't think you need to round that often, but a mid-morning round would be beneficial. I don't mean see every patient again, but just walk by their room and talk to their nurse to make sure the orders put in were executed, make sure the consulting team that was called earlier has stopped by (or not), and get an idea from the nurses how the patient is doing. Medicine is a 24/7 enterprise and things are always happening. Often, the intern doesn't have the time to go talk to every nurse so if the student does it and reports back with any major information they'll be contributing a lot to the team.
There's more but to me those three are the most important things a med student can do for the team and that actually teach the student something about being a resident and not a sponge.