Luffy first meets Nami in Orange Town , during the early part of the East Blue saga.

How Luffy Met Nami (Story Version)

Nami is in Orange Town trying to steal a treasure map from Buggy the Clown , targeting pirates because she hates them and makes a living robbing them. Luffy ends up dropping into the scene and getting caught up in her plan, and she briefly pretends he is her “boss” to trick Buggy and get closer to his treasure.

At first, Nami wants nothing to do with him once she learns he’s a pirate, and she even hands him over to Buggy and has him locked in a cage to protect her own goal. But after seeing Luffy’s strength, his attachment to his straw hat, and his unusual kindness—very different from the cruel pirates she knows—she slowly starts to change her view.

Later, when Luffy discovers the truth about Nami’s situation with Arlong and Cocoyasi Village, he fights Arlong to free her, and that’s when she officially joins the Straw Hat crew as their navigator.

Anime vs Manga: Tiny Detail

  • Manga: Their proper first meeting is in Orange Town, where they team up against Buggy’s pirates.
  • Anime: There is a brief earlier “eye contact” scene where they see each other much sooner (Alvida’s ship and then Shells Town), but they don’t really interact until Orange Town, which is considered their real first meeting.

So if someone asks “how did Luffy meet Nami?”, the clean answer is:
He meets her in Orange Town while she’s stealing from Buggy, and they end up reluctantly teaming up against his crew.

TL;DR: Luffy meets Nami in Orange Town while she’s stealing Buggy’s treasure; she initially uses and betrays him because she hates pirates, but after he saves her village from Arlong, she truly joins his crew.

Information gathered from public forums or data available on the internet and portrayed here.