You made it - Death Mountain lies ahead… or above, as the case may be. Make the climb carefully and see if you can get those Gorons to tell you anything about the Spiritual Stone of Fire.
Death Mountain Trail is pretty rugged, but nonetheless fairly straightfoward - it’s just a linear path that winds its way up to the Goron Village. You’ll run into the insect-like Red Tektites along the way, but the initial stretch is otherwise pretty uneventful. About midway up the mountain you’ll run into a suspicious-looking boulder, and next to it, another rock that springs to life when you approach! Turns out the living rock is a member of the Goron clan, the tribe that holds the Spiritual Stone of Fire, and the large boulder blocks off the Dodongo’s Cavern, their source of food. What a predicament!
Keep following the trail and you’ll eventually reach a spot where the path branches off a bit. You can either climb a steep incline and keep ascending the mountain or you can continue along the main trail to the Goron City. You can’t actually get up the mountain yet - large boulders block the way - so just keep going until you reach the entrance to the Goron Village. Watch out for the rolling Goron that rumbles by as you go - he’s trying to deliver a Bomb Flower to the sealed cavern entrance below so as to unblock it and it’s set to explode!
Goron City is built inside a giant multi-leveled cave pit that can be kind of confusing for first-timers. Luckily, most of it is sealed off when you first visit, and the place you need to get to is at the very bottom besides, meaning there’s little opportunity to get too lost. Feel free to explore wherever you’d like, but steadily make your way to the lowest floor of the pit.
There you’ll see a stone door of sorts marked with the hand-print symbol of the Gorons. Stand on the carpet set out on the floor outside of the door and play Zelda’s Lullaby to prove your connection to the Royal Family. This will cause the door to slide open, and you can proceed inside to meet the Gorons’ patriarch, Darunia.
Unfortunately for you, Darunia’s far from in a suitable mood to be handing out Spiritual Stones right now thanks to that boulder blocking Dodongo’s Cavern. Apparently Ganondorf is to blame - that would certainly explain the monsters prowling the mountainside. You’ll need some way to get Darunia to warm up to you - why not try using the song of friendship Saria taught you? Stand before him and play Saria’s Song and he’ll break into a wild dance that’s hilarious to watch.
Once he’s loosened up a bit, he’ll give you the Goron’s Bracelet, a legendary trinket that grants incredible strength to its wielder. He charges you with using this bracelet to pluck a Bomb Flower and find a way into the Dodongo’s Cavern. If you manage to fight off the Dodongos in the cave, he’ll give you the Spiritual Stone. I wonder why so many people think a little kid like you complete such spectacular tasks? (Not that you’re complaining!)
Backtrack up the many flights of stairs to the top floor of the city and head back out to the Death Mountain Trail. You can grab Heart Piece 7 on your way out if you’d like.
Once you’ve made it back outside, take a right and head for the nearby outcropping, which overlooks Dodongo’s Cavern. You can pluck the Bomb Flower here and chuck it over the edge of the cliff to blow up the boulder blocking the cave. It might take a few tries to throw it exactly the way you need to in order to strike the rock with the blast, but before too long you should have cleared the rock and opened the way inside.
Ocarina of Time screenshots courtesy of AceofSuns. Screenshots will eventually be replaced with 3DS version images, which are not presently available for hopefully obvious reasons.