Main Quest: Follow the Sheikah Slate
To find out where you need to go next, press [-] on your left Joy-Con and you will see a yellow dot marking a seemingly arbitrary spot on your map out to the east. Before we head there though, why don't we try talking to the old man? It's completely optional but might shed some insight into this desolate area.
To initiate the cutscene, pick up the cooked apple laying on the ground. Listen to the old man chat about the Temple of Time and keep that in mind for later. As you leave him behind and continue straight down the path, steal the Woodcutter's Axe near where he is sitting. It's sitting by a stump. You can use it to cut down trees and start building up a stockpile of firewood, or you can use it as a weapon to start building up a weapon kit.
Note: Feel free to kill the Bokoblin camps nearby, as their Clubs will help pad out your inventory. They aren't very strong or durable, but it's better than nothing.
Pass around the Temple of Time and find what looks like a strange structure embedded into a hill. Once you have gotten closer to the structure, find a hole at the bottom of the hill where you can fall down. There will be another pedestal. Examine it by pressing A. Enjoy the epic cutscene! Once the cutscenes have concluded, drop down the hole and use the platforms like "steps" so that you don't fall down and die.
The old man will meet you on the ground once more and tell you more about Calamity Ganon. Obviously the best course of action would be to destroy Ganon right now...but you have no way off the plateau without falling to your doom. Link will negotiate with the old man for his paraglider and you will receive your next main quest: The Isolated Plateau.