TrapperReady gives the most important tip, about safety. I'll repeat and add to it:
Make certain you know where all members of your group are at all times. When I hunt grouse in a group, we walk in a line, with no member of the group ever getting more than two or three steps ahead of or behind of the line.
Sometimes, when a grouse flushes, but the hunter doesn't shoot, he forgets to put his safety back on. Watch for this.
Be real careful if you come to an edge or open area. Usually grouse fly away from you, but they don't like to fly across wide open spaces, so if you flush them near an edge they'll often fly right back towards you or other hunters in your group. Be careful where you shoot.
Also be careful when you come out of the brush to a (dirt) road. A lot of guys seem to immediately want to walk across it real quick for some reason, getting in front of the others hunters still in the brush.
Take a compass. Use it.
Take water, especially this time of year.
Now that's out of the way, the best tip I ever got for grouse shooting is this: "Hurry up and take your time." Don't snap shoot wildly at the sound of the flush, but use good shooting form and get on the bird, but quick!
Have fun!
Oh, do you have a dog?