Unlocking characters to add to your party in Genshin Impact usually means you have to use various forms of currency. First, you need to go to the store to turn Primogems into Acquaint Fate or Intertwined Fate, which are premium currency systems. When you've had enough, you go to the wishes category of your main menu and use those fate items to make wishes, and you are randomly given characters or weapons based on the wish you chose to make. They vary for each option, and these pools will come in and out over time. A character, Barbara, is available to all players in the game for a limited time.
Any player who created an account before Genshin Impact officially released on September 28, and before the game's release Update 1.1 can receive Barbara if they reach Adventure Rank 20. Various story quests, tending to a handful of side quests, explore the world, fight monsters, and unlock chests after defeating enemies you encounter. It's about doing almost everything in Genshin Impact, so the more you play the game the higher your Adventure Rank increases.
Once you miss this opportunity, you will no longer be able to unlock Barbara for free. Instead, you'll likely see her enter the character pool in Wishes, which means you have to use premium currency to unlock her, and it might take a bit of time to access it.
When Genshin Impact update 1.1 released, players who created their accounts after the game was released, before update 1.1, have 30 days after update to reach Adventure Rank 20 . After that, the offer is definitely lost. You should receive Barbara immediately upon reaching this rank, so there are no additional steps beyond this point.