I still remember my first Club Championship after joining my current course. I can tell you this much.... It is not easy to simply try and convince yourself this is just like any other round of golf. You will undoubtedly feel the nerves over the first tee shot as the club pro hands you the card and you identify your ball to your competitors prior to teeing off. Even though you may not believe you are in the running to win simply because there are so many players with low handicaps than you, you will still feel the nerves. You will also likely feel the nerves on the short putts more so than on the long ones. That is simply because you have higher expectations on the short ones and are afraid to miss. All I can say to try and help you out (and this has worked for me) is set a target score that is a bit of a stretch, but no unreasonable for you to meet, and work towards that. Most importantly - remember this is supposed to be fun ! Embrace the challenge but enjoy the day. That will make it a lot easier to play well !!!! Good luck on your endeavour !

I remember my first Club C when I finally joined a course that had a Club Championship. I was so nervous. It was raining on the first day, and I was focusing on staying dry. It actually helped calm my nerves and I was one over after 4 holes. The rain stopped and I went on to shoot 87. Shot 83 in round 2 and ended up middle of the pack in C flight.
Keep reminding yourself that this is fun and just try and keep your nerves in check. Remember to breath.