General advice
There are two obvious aspects to doing time trials. Training and the event itself. There are three key training points: 1) Do 3-5 minute intervals at speeds above what you want to do in the TT, with 2-3 minute recoveries in between. Depending on your current fitness and desire, do as many as 5 intervals, twice a week with at least a day off (recovery rides) in between . You might also do a couple of 10-15 minute intervals (5 minute recovery) as well. 2) Have a good base of mileage before actually doing a TT (500-1,000 miles). The amount would vary with TT distance and your general fitness and cycling experience, but the longer the planned event, the more base mileage you should have to both perform well and more importantly, avoid injury. 3) Work on your position. Get as low as possible on the bike while still being able to breath well. Hold that position for long periods. If you're going to use aero bars, practice with them. And practice your turnarounds.
For the event itself, there are a whole bunch of little points which, when added together can both improve your time and make the TT a more "enjoyable" ride. Be well fed and well hydrated, with a good carbo intake the day before and the day of the event. If its an evening ride, snack & sip through the afternoon. Some caffeine 30-60 minutes before the ride doesn't hurt. Be well warmed up - the saying is the shorter the TT, the longer you should warm up. A 10 mile ride to warm up for a 10 mile TT is good. Shortly before your start, do a couple of "jumps" up to maximum effort for 1/4-1/2 mile to get your body ready for a fast start. Arrive at the line sweating, but not out of breath, and ready for a rapid acceleration up to TT speed. Try to get to your maximum sustainable effort ASAP (remember, you're already warmed up). If your legs seem like they are the limit to going faster, shift to a lower gear. If your lungs seem like your limit, shift to a higher gear. Get into your best aero position and stay there. For the turnaround, hold your speed as long as possible, jam the brakes and bank the turn faster than you think you can go. Forget this business about sprinting for the finish - you should have nothing left to sprint with. Around here, the finish of a TT is described as "notfarfrompukin" if you get my point.