How to prepare for a race in a short time?

"Training effect" is something that refers to how soon you can expect a particular workout to improve you endurance/fitness. The rule-of-thumb for distance running, is a training effect takes 3 weeks. So honestly, Ollie, in 3-days, no matter what kind of training you go out and do, it's likely going to be more detrimental than helpful in getting you ready to run 3-miles than if you went out and did it cold today. About all I can recommend is maybe trying to run a mile today, tomorrow and then try 1.5 on the following day. Take the day before the race off, take a long hot bath, keep loose, don't eat anything extreme or unusual. Keep hydrated, well rested and keep your sense of humor. If this is going to be a competition against runners that race regularily, your doors are going to get blown off and the back of the pack could be pretty lonely, so just keep putting one foot in front of the other, you'll get to the finish. Then next time you 'sign up' for something, give yourself a few months to prepare the right way and come back to the site here for a serious dose of advice.
Just curious...are you doing this on a dare? Or what's the motivation?

I'll second what he said. Whatever you do in the race is going to be based solely on natural talent. Training can't help you for a race in four days.