I'm assuming you are talking about a patient who is not just newly admitted to the service. If so, you should be vaguely aware of the basics from rounds on previous days (ie was the pt admitted for CHF, GI bleed, etc). You should also have a sense for if the pt has been improving, staying the same or getting worse during the stay.
So with that in mind, go read the H&P, and the previous day's note. (It's not necessary to go thru the whole chart ) Then you'll know what areas to focus on when you go see the pt. When you examine the pt, do a quick focused exam. Always make sure that pt is tolerating whatever kind of diet they have and that urine/gas is moving, and that there is no new pain, and that old pain is improving. (YOu probably know by now that pts often won't volunteer things) Then look at the vitals, I&0 and labs. I think a key with these things on a new pt is also to check the values from previous days, so that you know what the trend is (eg you find a Cr of 2.5....is that new or is it an improvement from 2.8, or perhaps it's the pts baseline). Also look up any other xray, echo, CT results if there are new test from those. It's probably only necessary to go through the previous days orders so that you can asertain what needs to be looked up and make sure it's all done
Then, write the note. You might start by using the previous day's note as a guide for which issues need to be addressed, and add any new issues you discovered. For example, a pts BP might be stable but there may be electrolytes that need replacing today.
For the presentation, take your cue from the residents and attending as far as the level of detail that needs to be included. If not much has changed with the pt, you may only need to say that he/she is doing well, and read the vitals and pertient labs (eg you'd be following the HCT for a GI bleeder, and you'd want to make sure lytes are OK for a pt on dig)
If you are being asked to see/present a new pt, it's often quicker to make a copy of the H&P and present from that (don't just read it, however, but refer to it). Your note could take the cue from the plan section of the H&P, only focus on areas that needed intervention, plus any new complaints the pt has.
Hope this helps! It just takes some experience to develop a routine.