Walk down the hall to the report room laying eyes on all your pts, see who looks scariest. Get report knowing who you are most concerned about based on that, and finding out about any others. Go to your sickiest patients (could code if something has changed that isn't picked up on) and introduce yourself and do a problem based assessment, see if they will live for the next hour
(you may end up doing the whole assessment just because they are so sick or so involved). Once you've confirmed that your sickest are OK then go on with the rest of your group. On nights you may find it good to see the sickest first because you may catch the families, or can call the doc with any concerns before they go to bed. You may also get a run down on the plan of care if you call the doc early, if you wake them in the middle of the night they won't be as forthcoming.
After the sickest are seen I go to those that are least sick, just so I can do them up and cross them off the list. Then you know how much time you have to spend with middle pts, are you just going to make sure they don't die tonight or can you give them a full spa treatment? Some may want to chat, or request something extra, you will already have a good idea of what you are dealing with tonight, and whether you have time to squeeze it in.
And always listen to pt's and families if they feel something has gone very wrong and do an extra careful assessment on them. They will feel reassured and 9 times out of 10 they are right. Most of the "saves" I've made have had something to do with pts/families picking out the subtle signs, and then watching carefully.