There are four Goron Elders in Twilight Princess.
The First Elder
The first one is found after you fight your way up Death Mountain and come into a room full of Gorons. Just before they all attack you, the Elder stops them and challenges you to a sumo wrestle. After defeating him, you are granted access to the Goron Mines.
Goron Mine Elders
The Goron Mine Elders have a piece of the Big Key. Since there are three pieces, there are the three other Elders. The first (technically the second) one is met after you go through a room in which you have to pull a huge piece of the wall out and get past before it closes or your crushed. The second elder is found in another room later in the dungeon which tells you about the Hero's Bow. The third is found after you defeat all the Beamos in the room after you get the Hero's Bow. You pull out one of the Beamos and you find the third elder.
The very first elder is somewhat smaller than younger Gorons. However, he is the most muscular out of the four. The second elder is smaller than Link, possibly about as tall as Talo. He is holding a stick in his shaking hand and seems to be on fire. The third elder is a bit taller than the second and has an elongated face, he also talks like a hippie. The fourth one is in a meditating pose and looks the most human like out of the four. He says he premonitioned Link coming to him.