What time should I show up to my triathlon?
The exact time you should get to the race before the start varies widely of course. It depends on the logistics of the race (e.g. how far you need to walk to the swim start) and what's required by the organizers (e.g. transition closing times) so it's not possible to give hard and fast rules. What I do suggest is making yourself a mini-schedule so you can make sure you have enough time to warm up and get to the start line not in a panic. Having a schedule also means you can avoid being there too early missing out on precious sleep time and standing out in the morning cold with nothing to do but get nervous. I also suggest timing the warm up so it's nice and close to race start. If you're riding your bike an hour and half before the start you're body really won't remember it by the time you get on the bike for the real thing.
Here's an example for a 7am race start:
5:30am Arrive at race site parking
5:40am-5:55am Packet pick-up
6:00am-6:15am Transition Set-up
6:15am-6:30am Bike warm up. (if transition closes 6:30am - check this)
6:30am-6:45am Get wetsuit on, porta potty, walk down to swim start
6:45am-6:55am Swim warm up.
7:00am Race Start
Having a rough schedule written down or in your head will help you reduce stress before the start and give you time to get everything done that you need to.