Unlocking characters to add to your party in Genshin Impact means typically you need to use various forms of currency. First, you need to go to the shop to turn Primogems into Acquaint Fate or Intertwined Fate, which are premium currency systems. When you have enough, you go to the wish category in your main menu and use those pieces of fate to make wishes, and you randomly receive characters or weapons based on the wish you chose to make. They vary for each option, and these pools will shift in and out as time goes by. One character, Barbara, is available to every player 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 releases, it’s 1.1 update can receive Barbara if they reach Adventure Rank 20. Making it to Adventure Rank 20 mostly means playing through the game, going through the various story quests, tending to a handful of sidequests, exploring the world, battling monsters, and unlocking chests after defeating the enemies you encounter. It’s all about doing nearly everything in Genshin Impact, so the more you play the game, the more your Adventure Rank grows.
Once you miss this opportunity, you won’t be able to unlock Barbara for free. Instead, you will likely see her enter the pool of characters in wishes, which means you need to use premium currency to unlock her, and that can take quite a bit of time to access.
When Genshin Impact’s 1.1 update releases, players who created their account after the game released, before the 1.1 update, have 30 days after it to make it to Adventure Rank 20. After that, the offer is gone for good. You should receive Barbara immediately reaching this rank, so there are no added steps beyond this point.