So the medicine approach ....
For old patients:
This is Mr. Jones, our 55 y/o male (+/- the diagnosis, depends how well the team knows him). He had an uneventful night and is without complaint this morning. His vital signs are afebrile, pulse 92, RR 18, BP 126/72, POx 98% on RA. His Is/Os were xxx. He had XX BMs yesterday (for narcs or possible c diff). His weight is xxx (for heart failure, volume issue patients, etc). His exam findings are [some attendings want a full exam, most just want you to focus on the pertinent system(s)]. His labs from yesterday (or any back in the am) are. Yesterday's diagnostics tests/consult recs were .... In summary, he has xxx and my plan today is: [some attendings will accept a one/two liner here, others will want a complete systems based approach].
You have to taylor this to your patient and your attending. There is a fine line between so much info the team's eyes glaze over (but be warned, some attendings want that and you are rarely faulted for saying too much).
Admission notes, you all know the pattern. In terms of what questions to ask for each patient, that will come with time. You kind of have to listen to enough history to get at a reasonable differential and then go from there. As a med student, I recommend just taking the system he is complaining about and exhausting the history for that. Actually, I pretty much do that now anyways.
PLEASE practice before you present. I always make my med students present to me or the intern prior to rounds with the attending. We should be able to guide you if your organization is going astray etc.