To unlock characters in Genshin Impact, you need to acquire Wishes. These wishes are first shown to you when you first walk through history before visiting the various temples and challenges surrounding Mondstadt. The first wish you use in the game is given to you at the start of the game, for free. However, after all, you still have to use this method to unlock other characters, but it comes at a price.
To receive additional wishes in Genshin Impact, you must use Acquaint Fate. This is a premium in-game currency that you can rarely acquire while playing the game. There are a handful of Adventurer Rank rewards that give you this currency. Otherwise, you have to pay it directly using the Primogem you acquire by going through various achievements and stages in the game. It costs 160 Primogem to buy a single piece of Acquaint Fate or Intertwined Fate. Both are a premium currency.
If you want more Primogems to purchase additional Acquaint Fate or Intertwined Fate, you can purchase them from the store using real money. It's a faster way to receive additional characters and gear than playing naturally with Genshin Impact.
When you have all the premium currency, you want to buy on your profile, go back to the main menu and go down to the wish category. It should be the third option. When you view the Wishes option, you should see all of the available options. For every wish you want to invoke, it costs an Acquaint Fate or Intertwined Fate. However, some of the purchasable options have increased chances if you go for a larger plan. For example, you have a guaranteed chance of receiving a four star character or weapon by using 10 Acquaint Fate. This is a better deal, but it does mean you may have to wait longer to purchase this set.
