how to run a faster mile

Start with a pre-race warmup. Do a few paced sprints to get your heart rate up. Mentally go through the race in your head. Know what times you want to have at each lap.

Run as quickly as possible on Lap 1. You’ll want to start out a little faster than what is necessary to get your target time.

Psychologically, you're going to slow down as you get further into the mile, so make sure this first lap is good to compensate. At the same time, don't spend all of your energy on this lap.
A good example would be, if you want to run a 5:00 mile, each lap would need to be 75 seconds. A good time for your first lap would be 71 to 73 seconds. It's not too fast, but it's fast enough to give you some security.

Run Lap 2 at a comfortable pace. This is the lap which should be right on target. In the 5:00 minute mile we mentioned earlier, Lap 2 is the lap which should be exactly 75 seconds, so your time at the halfway point should be 2:26-2:28.

If you've been running 400m sprints, then you'll know the exact pace that you need to run this lap. You'll feel your body's muscle memory click into place.
Your adrenaline rush will probably start to wear off midway through this lap, and you'll start feeling it. Stay focused on maintaining your running form and keeping up your pace.