In the context of a foot race (though the first three options apply to swimming, biking, etc):
If you have three days to prepare you can beat someone who is in much better shape and much faster. Here's how:
Option 1: EPO: EPO is a natural hormone that your kidneys make. It tells your bone marrow to make a bunch of red blood cells. If you buy synthetic EPO or genetically engineered EPO you can give it to your self and you will make more red blood cells than normal. This will allow you to transport more oxygen to your muscles. This means that your muscles will not fatigue as much or as fast as they would normally. This is very safe if taken in the right dose and will give you a large advantage.
Option 2 blood doping: Another way to get extra red blood cells. 1) remove your own blood and store until the race. 2) right before the race give your self an infusion of your stored blood. -- this option is much more dangerous, but cheaper and arguably easier to do. This will also give you a huge advantage, but it could lead to stroke or heart problems.
Option 3 violence: If you're really desparate, you could always trip them, gnaw their foot off, or otherwise incapacitate them.
Option 4 (for those with a smaller sense of humor) the honest way: This rarely works, BUT if you have long enough to train, you could try to get in shape.
Go buy two pairs of shoes: 1)running shoes with good support to train in 2)flats with no support and no weight to run in.
Plan your workout according to how long you have, how far you have to run, and under what conditions (relay, hills, flat, on grass, turf, ...). Try to run everything that you will on race day.
Don't run too long on pavement or a rubbery track if you are just training. This can cause shin-splints (where the muscle begins to tear away from your shin) as well as backache and other problems.
make sure you bring water and sweats to use after the race
Run with someone of roughly your ability or better. Running alone is usually slower and harder.
You should take the day or even a couple days before the race off.
Make sure you stretch and run at least a little to warm up.
When you race, wear shorts (and no boxers guys... you'll regret it if you do that) unless it is really freezing then use spandex.
See blood doping for more details.