how a meteor gets into your world
The first crash is free. Kill your world evil boss, whether that is the Eater of Worlds in a Corruption world or the Brain of Cthulhu in a Crimson one, and a meteor is guaranteed. Finish the fight in the small hours before dawn and it lands immediately. Any other time of day and it waits for the next midnight, which is why the usual experience is beating the boss in the afternoon and hearing the announcement hours later while you are busy with something else.
After that the world keeps rolling on its own: a two percent chance every midnight, forever. Over a long playthrough that is more ore than anyone needs. If you want more sooner, kill the world evil boss again. Each repeat kill is a coin flip to schedule a crash, and the flips stack inside a single day, so three kills before midnight leaves you seven chances in eight of a meteor that night. Only one can land per midnight though, no matter how many rolls you win.
Kills made between midnight and dawn are the exception. Those crash on the spot, so repeating the fight in that window can drop several meteors in one night.
finding the crater
The meteor you see streaking across the background at 11:40 PM is theater. It does not tell you which half of the world the rock actually hit, and it plays even on nights where nothing lands at all. Ignore it and go looking.
The placement rules rule out a lot of ground for you. A meteor never lands inside a protected column around your spawn point, which reaches eight percent of the map width out in each direction and is wider than most people assume. It needs a dense patch of solid tiles, so it skips lakes, the Ocean and most of the Jungle. It counts Cloud and Sunplate blocks heavily against a site, which is why Floating Islands are never hit. And it refuses to appear anywhere a player can currently see.
That leaves ordinary surface, plus two places people forget. If nothing is on the surface, check inside a Living Tree or down one of the Corruption or Crimson chasms. Given a clear vertical drop the rock can fall all the way into the Underworld.
mining it without dying
Standing on Meteorite sets you on fire. The Obsidian Skull, or any of the accessories built from it, removes that outright and should be equipped before you swing a pickaxe. Meteor Heads are the other half of the problem. They fly straight at you through solid rock, so walling yourself in achieves nothing, and no amount of nearby NPC housing suppresses them.
Their spawns are tied to the ore itself. The area stops counting as a Meteorite biome once fewer than 75 blocks are left, so the fastest route to a quiet crater is to mine hard rather than to fight. Meteorite needs 50 pickaxe power to break: silver falls just short, tungsten scrapes in, and gold or platinum is comfortable. The Bone Pickaxe from the Skeleton Merchant is the quickest option before Hardmode, and a Mining Potion or the Ancient Chisel trims the trip further.
what the ore is actually for
One recipe justifies the whole trip. The Space Gun costs mana like anything else until you put on the full Meteor Helmet, Meteor Suit and Meteor Leggings, at which point it costs nothing and you can hold the fire button down indefinitely. Nothing else this early hands a class free ammo on a weapon that fires as fast as you can click, and it carries a mage straight through to the Wall of Flesh.
The rest of the tree is worth a look and not worth farming for. The Star Cannon hits absurdly hard but eats Fallen Stars, so it is a burst weapon limited by how many nights you have spent collecting. The Meteor Hamaxe is a decent tool. Phaseblades are mostly a gem sink.
protecting what you already built
Crashes wreck terrain and the game does not care what was there first. Two cheap wards exist. Any placed chest blocks a landing within about 35 tiles horizontally and vertically, so one chest dropped near your base, the Ocean, a jungle entrance or an underground desert opening keeps meteors off it permanently. Mannequins, hat racks and pylons do the same job, and a handful of cloud or sunplate blocks works as well.
If you are done collecting entirely you can switch the event off. The game will not spawn a meteor while too much Meteorite is already placed above 0 feet on the depth meter, and the ceiling is roughly 400 blocks on a small world, 610 on a medium one and 800 on a large one. Stack your surplus in a wall above ground and the midnight interruptions stop for good.