A few tips from an old guy who hasn't gone down in a long time... and that is not by happenstance:
Lose the tri-bars: The best way to sew the seeds of uncertainty about your riding skill and experience with a new group ride, is to show up with a pair, or worse still a full Tri/TT bike.
Watch, listen, and learn: Every group has it's methods of communication. Most are ubiquitous and universal, but some are specific and local. Sit in and watch to make sure you speak their language before you deign to pull through.
Never "half wheel"!... A rookie move at it's worst. Racing in a pack and training with a group are very different. A group works together to move efficiently. Your job riding next to another rider is to make sure that your hips, elbows and handlebars align with his. Should you bump each other (this can and should be practiced) you will bounce off each other and remain upright. If your half wheeling at that same moment, you're both going down.
Don't watch wheels: You need far more situational awareness than just the distance to the wheel you're following. Find a comfortable and efficient distance to that wheel. Look up!... focus on that riders body. Imprint on that distance and use it as the measure of your comfort zone. You will now be able to look up the road and see other concerns and aspects of the ride and the group dynamic, and intuitively understand and monitor when you are getting too close.
Drive a tractor trailer: When you do eventually get to pull through with your group two big rookie mistakes are, accelerating off the front, and pulling in too quickly after passing obstacles or slower riders. The former will disrupt the group and earn some grumbles if not epithets from behind, the latter will put somebody at the back in a perilous situation. When you are at the front, you're essentially driving a long tractor trailer. Keep it in mind and drive responsibly.
Exit Strategy: One thing too always keep in the back of your mind is an exit strategy. Should a squirrel attempt suicide in front of your paceline, things are going to happen quickly. Braking hard is generally your last and worst option. If the terrain off the shoulder is more inviting than the on coming traffic lane at any given moment, is a good thing to be aware of in a crisis situation.
Talk to me: Always ask about anything that you do not already know about how this particular group rides. The gain is twofold. Your understanding and general safety is insured, and you build more trust from, and acceptance by the group.
General rule: Your most important job on any group ride is to make sure that no other rider hits the pavement as a result of any action that you may take. It sounds simple, but it is the golden rule of group riding. If everyone in your group rides this way it promotes safety, communication, and establishes solid rider etiquette from which we all benefit.