Hi Liz,
I would aim to arrive at Disney's Animal Kingdom theme park by no later than 7.40am on the day of your 8.00am dining reservation.
Once you arrive, simply head over to the park entrance turnstile open for guests with early breakfast reservations. To help you find your way, look for a sign that says "Breakfast Entrance" or "Character Breakfast" (or something similar). This turnstile can usually be found at one of the far ends of the turnstile row. If you don't spot the special breakfast entrance right away, simply ask a Cast Member to point you in the right direction.
A Cast Member at the breakfast entrance will take your name to confirm that you have a reservation and will admit you entrance to the park with your park ticket.
Although I have never been asked to provide any other proof of having a dining reservation, I would definitely recommend that you bring a note of your confirmation number just in case.
Be sure to have your camera at the ready as you make your way through the park to the restaurant as this is a great opportunity to have some photographs taken in front of the Tree of Life without any other Guests in the background.
Wishing you a magical holiday filled with memories which will last a lifetime!