For any new triathlete, the swim is without a doubt the hardest hurdle to overcome if you haven't come from a competitive swimmer background. There is no doubt an advantage to having years of laps in a pool and swimming races when you line up in open water. But, being a non-kid swimmer myself, sometimes these expert swimmers don't quite understand what anxiety this leg brings to a non-fish. Having panicked HARD in my two first races I developed a plan to try and overcome.
One, plan to buy a wetsuit. The buoyancy you get from this is measurable. The first time you get one and go into the water, you will feel like you are popping out up to your chest like a channel buoy. You can get a decent sleeveless wetsuit for $99-$150 that is cheap insurance. Not only does it help you float, and keep you warm, it helps you swim a little bit faster too!
Two, on race day, get into the water before the race and get your face wet. Acclimating to the water temp is very helpful to overcoming the initial shock of getting into the water for a scrum with 50-100 friends. Also, during acclimation, pull on your suit to make it as comfortable as possible on your chest. I find that in putting on the suit sometimes, it doesn't come up my legs enough and the arm straps are pulling down too tightly. Pull up on the crotch of the suit to get more of it up into the upper body and relieve this pressure. If you can't get into the water before the race, wade in at your start slowly and take a few seconds before starting.
Three, don't fight the crowd. If the first turn is a left, line up on the right side and slowly start off. Lining up with the crowd only lends to increasing anxiety as you bump and collide with other swimmers. Quick geometry says that you are adding only a minimum of meters by doing this. Racing in calmer waters will help you relax and get into a rhythm. In most cases, things will bunch again at the first turn if it is in the first few minutes if the swim and then string out. Some races offer streaming starts where 3 people start every 10-20 seconds. This is an amazing development for new racers. Check this out if you need it.
Four, be as fit as you can. Swimming 2-3 times a week is the best way to get fit for a minimum of time. If you are just starting, swim a portion of the race distance for a few weeks and then work your way up. Your first triathlon should be a sprint or Olympic distance. That way, you are swimming 500-1500 yards in the race. When starting, if you haven't been swimming in a while, swim as many laps as you can consecutively, and then take a 30-60 sec break. In the race, this could be simulated with swimming freestyle a bit and then popping up for a few seconds of breaststroke to get your bearings and breathe if required.
One thing the start of a race brings on is panic in many. Being out of breath compounds this. After swimming for a few weeks, integrate what I call a start drill into your workout. After a warmup of 200-500 yards, do the following:
2x50 yard sprint with 5 sec rest after each
2x100 yard swim at your pace with 15 sec rest after each
Repeat this 2-4 times
This workout gets you breathing hard, and then you have to turn right around and swim a consistent 100yd while managing your breathing. The first 100 in each set is what I have found best simulates open water starting. This ability to swim and manage breathing will give you confidence when you have that feeling in a race.
Hopefully you can put these few things together to help your first swim. Triathlon is a great sport that requires a lot of skills that produce great overall body fitness. Completing your first open water race will also give you the confidence and mental toughness that will help in many other situations in life.