Bare essentials:
Have a bucket,
Have a bottle of Water
Have a clean white Towel,
Have Vaseline (Petrolium Jelly)
Have a Bottle of water with a spray nozzle on it.
Have an Ice Pack.
Have some tape to secure loose bandages.
Have your boxers Gumshield and Medical card.
FIRST AID KIT (Just incase you need it. I've been to too many shows not well organised enough and you can't get hold of things like plasters etc without disturbing either the doctor or paramedics. Something you shouldn't have to do.)
Before the fight:
It is your reponsibility that your boxer gets to the venue in time for the weigh in. He shouldn't have to drive there if it's a long distance.
When you get to the event, get your boxer to the weigh in and get him checked out by the doctor. Give the medical card to either the organiser or the doctor at the weigh in.
Get your boxer relaxed and then warmed up and ready (apply vaseline/bandages etc) in ample time for the bout. (If you need details about this then ask).
Your boxer should not have to worry about wether he has his equipment with him or not. You as the corner should insure that he has everything he needs, especially if your only cornering one fighter on the show.
When you get to the ring:
Give your boxer any last minute instructions, i.e. go over his gameplan in as few words as possible. If it is simply to run and counter then just say run and counter.
Between rounds:
You are not allowed to talk to your boxer while the bout is taking place. I.e. during rounds.
Between rounds, only one cornerman enters the ring and only that guy talks.
Sit your boxer in the corner in a relaxed position(some prefer to stand).
Take his gumshield and give it to the guy out side.
Guy outside should rinse it off and hold on to it.
Guy inside should offer the boxer some water and spray him down and clean him up. Wipe away water etc.
Give him some instruction in plain and simple terms. The less words the better. Try not to shadow box and be all frantic telling him to do this and that. he wont remember any of it.
Give gumshield back to guy in ring and put it in boxers mouth. Make sure boxer is cleaned up and dried. Make him look presentable as it will psychologically effect his opponent. Also I have seen bouts stopped by doctors where a little blood from the lip or nose has mixed with sweat and water and turned a white vest red. only for the doctor to crap himself and stop the bout.
Leave the ring.
After the bout:
Take of boxer gloves, headguard, gumshield. offer water towel dry, clean up etc.
Tell your boxer to shake hands with opponent and his cornermen.
Get you boxer to the locker room. get him relaxed. Celebrate your vistory if you win

Do not put him down even if he deserves it. That can wait for when your in the gym.
get him home.
Hope this helps.