On Race Day
The transition area is like your home base. It's tempting to spread out and make it comfortable but you do need to respect your fellow athletes. Because of the limited space, you should have only what you need, and no more, to make the change from swim to bike and bike to run.
Before the triathlon start, walk the transition area: Take mental note of the swim start/finish, the bike in and out, the bike rack position, the run exit, and finish line. That's a lot to do, but it can make a difference in your overall time and comfort level. Knowing where you need to go settles the mind so you don't get distracted by the commotion as you exit the water, get caught in the flurry of cyclists as you transition off the bike, or make the mistake of running out in the wrong direction.
The Swim Exit
The swim finish and transition is not the time to get excited. Avoid picking up your intensity when coming out of the water. Rather, start to prepare your mind and body for the next event.
Physically, it is time to switch from swimming to cycling muscles. The end of the swim begins the change of a horizontal to a vertical body position. When swimming, particularly in wetsuits, blood pools in the arms, chest and shoulders (there's not a lot of kicking in a wetsuit). This concentration of blood now needs to move down into the cycling muscles. The transition run (from the water to the transition area) can help this conversion if you remain calm and avoid sprinting.
Toward the end of the swim, try lengthening your stroke in the front end (entry to downsweep) and, reduce the intensity of the pull. You can increase the kick during the last few meters to compensate (not to a sprint, but add just a bit more motion). Several breaststroke or butterfly kicks are also very effective just before exiting the water, as they also can help increase the blood flow to the legs.
From the swim exit, you should unzip your wetsuit while jogging, and remove the arms (depending on the length of the run-up from the water). Once at the bike, remove the rest of the wetsuit. The most efficient method is to pull the wetsuit down towards the ankles and then step on one side, lift the other foot out and then step on the free wetsuit leg and lift that foot out.
The key is to practice before the triathlon and over time the skills mature into a familiar and comfortable transition from swimming through the transition run and into the bike.
First, know the rules! Transition areas have a distinct order with spaces specified for certain things, including zones for mounting and dismounting. Be sure to know what each of those areas is for and familiarize yourself with the sanctioned rules of conduct for your own safety and for the safety of others.