1. Gradually increase the length of your run. Work up to about 6 miles and 3 miles will seem like a piece of cake. You will build your endurance and aerobic capacity. 6 miles may not be an option right now, but even 4-5 miles will boost your speed when you run 3.
2. Do some speed work. You can go to a track for this, or map out your own little 1/4 mile or 1/2 mile route. Warm up for about 10 minutes, then run 1/4 mile to 1/2 mile fast (race pace). Then run 1/4 to 1/2 mile recovery (nice easy pace). Repeat this until you've run about 3 miles. Don't forget a cool down jog. As you get stronger, you can increase the interval. Instead of a 1/2 mile, you can do mile repeats, etc. Speed work hurts...not gonna lie...but it really does work. You will be faster.
4. Add in some strength work. On the days you're not running, do some push-ups, squats, lunges, etc. Choose strength exercises that will work core and leg muscles. This will prevent injury and make you an overall stronger runner.