Essentials are good running shoes and water bottle.
Your feet are your running foundation and solid contact with the ground is important for safe trail running. It is essential to have good, properly fitted shoes designed for running. Should you have shoes specifically designed for trail running is a question that you should consider. Trail shoes typically have aggressive tread more appropriate for varied and potentially slippery conditions. They are also typically heavier and designed to support and protect your foot better on more rugged terrain that may include rocks, sticks and other obstacles on the trail.
Hear it again? Water hydration while active is a smart thing! People have varying opinions on carrying water during a run. The best solution to this can depend on the weather and how long you run. But at a minimum, you should bring a water bottle to your start/finish location.