Everything you need to know is in the regulations
http://www.worldcubeassociation.org/regulations/ but basically, when your group in the 3x3x3 event comes up you'll be asked to hand in your cube to the scramblers and you will need to go and wait in the competitor's area (out of sight of the scramblers!). When your cube has been scrambled a judge (usually just another cuber from another group) will bring your cube (hidden), call your name (if necessary), and you will take your place at one of the competition timers. You can let the judge know if you're unfamiliar with the StackMat timer and they'll tell you what you need to know. When you are ready (the judge will ask you) the judge will reveal the cube and you will be given 15 seconds to examine the cube (without making any solving moves of course). You will have to start the timer and start solving within those 15 seconds and so the judge will give you warnings of when 8 seconds and 12 seconds have elapsed. You solve the cube (hopefully!) and then stop the timer. Your time will be recorded by the judge and you may have to sign the scorecard if there's a penalty. This will all be explained to you as long as you let someone know you haven't done this before. You will enjoy it (that's not a requirement, it's a prediction!)