How Can I find Meteorite Ore?

Meteorite ore comes from the "Meteor" event, which in turns comes from breaking Crimson Hearts (or Shadow Orbs in Corruption worlds), and (in 1.4) defeating the boss summoned thereby.

In order to reach them, you will most likely have to break the crimstone blocks surrounding them, and for that, you have two options:

• Purification powder: If you have unlocked the Dryad (by defeating a boss), build her a house and buy purification powder from her. This will transform Crimstone and Ebonstone into regular Stone, which is easily mine-able with your copper pickaxe.
• Dynamite: Dynamite can either be found in chests underground, or purchased from the Demolitionist. If you're going the latter route, you will need to acquire explosives (grenades are easy enough to find in pots), and build a house for him to move into.

Once spawned, Meteorite ore requires a 50% pickaxe power pick to mine, which means Tungsten, Gold, or Platinum pickaxes are necessary. (Others are available, but these are the most easily accessible)