The general principle of the Vanderbilt start is that most boats broad reach at about the same speed that they close reach. So, you position the boat near the point where you will want to cross the starting line at the gun. Check your watch to see how long it will be until the starting gun. (Suppose you have 2 minutes until the start.) Sail on a broad reach away from the line for about 45 secs. Turn 180 degrees (It'll take about 20-30 sec. to turn and accelerate up to speed.) and sail toward the starting line at about a close reach. You should hit the line pretty close to the gun. Given a choice between being a little early or a little late, I'd rather be a little early, because, if you're early, you can always "put on the brakes," or bear off down the line, but if you're late, you're just late.
You shouldn't be mechanical in executing the Vanderbilt start. Be flexible. For example, when broad reaching away from the line, you should usually work your way a little more to windward, so that you have room to modify your approach slightly to accomodate other vessels approaching the line, or to squeeze out a barger.
As far as the math is concerned, take the total amount of time that remains until the start (2 minutes, in the above example), and divide it by 2. That gives you one minute. Then subtract about 15 seconds from it. That gives you 45 seconds. Broad reach away from the line for 45 seconds, turn 180 degrees, and head for the line. Easy, huh?