Disclaimer: Tolkien's the genius, not me.
It was a slow process, working out how to write again with a missing finger. Frodo hated even thinking about it, though the absent finger ached sometimes. But he practiced writing by taking notes while listening to Merry and Pippin or Gimli and Legolas tell of their adventures after the Fellowship’s breaking.
Uruk-hai, Ents, eagles, fallen wizards, great battles, and pirate ships – and Gandalf returning from the dead. So much had happened in so short a time!
When he grew frustrated with his clumsy writing, Frodo thought of how thrilled Bilbo would be with all these stories to write down.