Prior to Journey’s End, meteorite could be obtained pretty early on in the game. All you needed were a few bombs and you could blow up Shadow Orbs, but this will no longer spawn meteorites.
To get meteorite, you need to kill the Eater of Worlds. Then you need to mine it with a Tungsten or better pickaxe.
To get meteorite now, you must first defeat either the Eater of World or the Brain of Cthulhu. You can break all the shadow orbs in the world, but no meteorite will spawn until you’ve defeated one of these bosses at least once.
The bosses can easily be spawned by breaking either 3 Shadow orbs or 3 Crimson hearts. After you’ve beaten the boss, the meteor is now able to spawn in your world. Every time you beat the boss again, it’ll increase the chance of a meteorite spawning after midnight.
When it finally does spawn, you’ll see a notification at the bottom right telling you that one has landed. You can sometimes see it on the map, but the easiest way to locate it is just to run in a direction until you find it.
Journey’s End also made meteorite impossible to be mined with bombs, so you’ll need to use at least a tungsten pickaxe to mine it. Touching the meteorite without an obsidian skull equipped will burn you, so try to get one before you harvest a meteorite.