Wow, fun topic
I like reading people's responses so far.
For me I would say that I:
1) Practice a lot beforehand so that everything about your solving becomes muscle memory. This will help you be able to know what to do even when you're under pressure.
2) Practice some in public before the competition (at a coffee shop, in the mall) to get used to the nervous feeling of cubing in front of others. Don't worry about your times when you do this, you're practicing cubing in PUBLIC, not cubing FAST in public.
3) At the competition on the day of, try not to talk to people between solves. It's nice to talk to people yes, but if you talk to people between solves you lose your focus. Put on your blindfold/earmuffs/headphones etc. to make it obvious that you're concentrating right now and don't want to talk to anyone.
4) Remember a time in competition that you got really, really nervous and did not perform well - then don't do that this time. I know this sounds a little weird, but it helps me. My worst ever solve was my second solve in the 4x4x4 round at the 2003 world competition. My mind completely froze up blank and I felt like I completely forgot how to pair edges (I didn't have the procedure down as muscle memory, see #1). My solve time was literally almost double my usual times because once I realized that I was freezing up I began to panic, and this made me freeze up even more which made me panic even more. Once you know what this feeling feels like, you can recognize the first signs of it again. If you ever feel yourself start to freeze/panic again then just take slow deep breaths and allow yourself to calm down. Don't let yourself get into "red zone", allow yourself to calm down.
5) Compete inwardly, NOT outwardly.
Competing inwardly means to compete such as to beat your own personal goals, as they relate to your times only. Try to beat the result you got at the last competition (beat the time you got, NOT your placement in the competition). Try to beat your pb single or average, etc.
Competing outwardly means "
I will beat
YOU". An example is "I will place in the top 10", or "I will podium", or "I will break the WR". Competing outwardly is VERY stressful, but competing inwardly is not as much.
6) Do whatever it takes on competition day to help focus. For me, this now means wearing blinders and earmuffs during most of my solves. It looks crazy/stupid/strange whatever you want to call it, but it helps me focus. If it helps me focus, then I use it. I broke my pb 3x3x3 average record at Worlds 2011, in large part because I could only see the cube in front of me during my solves, which helped me focus. I also got both 5x5x5 BLD solves successfully, and at a large competition with high stakes. I haven't done that since 2006 at US Nationals. In short, yes I look stupid wearing all that crap on my head, but I don't care. It helps me focus, so I use ALL of that stuff.
Find what helps you focus (that is allowable by the WCA regulations of course) and USE it.
When you've competed 89 times, you don't get nervous.
