What are some tips on how to be a good Private?

Yes. First thing you want to find for yourself is some map grids. The more you collect and give to your sergeant the more likely he will think you've got it going on.

Just remember when someone's yelling at you for anything just tell him you're all f***** up sir and it'll usually get you by promise

The biggest thing is breath ! Like everyone is saying ask questions watch what others do. Be yourself. If you get overwhelmed tell somebody we all were there at one time

Like others have said keep your eyes and ears open, mouth shut (unless it's to ask questions). Learn as much as you can. 15 minutes early is on time, on time is late, if a formation is at 0900 be there in the right uniform and squared away at 0845. Pick and choose your friends carefully. Just as there are E-1 though E-4 that would stab you in the back, there are some NCO's that will also. Don't go out and buy a car with your first pay check. Don't be a barracks Rat. Yes you have a lot to learn and it'll seem like you are getting hit from all sides at once, but you need to have some down time to unwind, relax & recharge your batteries. Have your uniform for the next day ready before you go to bed.

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IS this an obvious answer to the question the way it was worded? Obedience really would help the private in question. When I was in the Army they only asked me to do what I was supposed to do, anyhow.