Group Ride Tip #1: Use proper hand signals when on the front
Debris in the road? Point it out. Turning left? Signal left. Coming to a stop sign or light? signal to slow or shout "slowing." These are at a bare minimum what is expected. If you are riding on the front, you are responsible for the rest of the group behind you. That means not dragging them into gravel unexpectedly or blasting them through an intersection.
Group Ride Tip #2: No surging
If you can feel your power going up and you're working harder, you're probably putting too much stress on the group. That is, unless the point of the ride is to go hard, but that's a different story. This is something most felt on uphills. If you're going notably harder on an uphill, you're more than likely going to string out the group and mess up the ride.
Group Ride Tip #3: If on the front, pedal down the hills.
If you're on the front and coasting down the hill, you're messing up the ride in most cases. On the front, you are facing more headwinds, so it's incumbent upon you to continue to put out a similar power down the hill as you did up.
Group Ride Tip #4: Do not half-wheel.
What is Half-Wheeling, you ask? Well, when you're on the front of a double paceline, the handlebars should be lined up and parallel. If you're half wheeling, think of your handlebars lining up with the leading edge of your cycling buddies front wheel.
Group Ride Tip #5 Regroup at the peak of large climbs.
This tip is somewhat dependent upon what the group has already agreed upon. But it is common that larger groups might split up on longer climbs. If that happened and the group has a 'no-drop' policy, be sure to wait and grab a couple of great pics at the top of the climb.
Group Ride Tip #6: No sudden braking
Braking should be an absolute last resort when riding in a group. There are even some disciplines of cycling that ban the use of brake levers entirely -- track cycling. So if you can avoid it, try not to grab a fist full of brakes at any time.
Group Ride Tip #7: Ride how you would like others to ride
If you notice a fellow rider doing something silly or that makes you nervous, make a mental note of it and don't do it.
Group Ride Tip #8: Hands on the bars at all times.
It might look cool to ride with no hands, but when you do it, you put the whole group at risk.