In Genshin Impact you use Primogems to purchase either Intertwined Fate or Acquaint Fate, which are what you use to wish for more characters. You can purchase Genesis Crystals (which convert into Primogems), but you can also earn plenty of Primogems in-game by opening chests, completing events, as well as doing Spiral Abyss, and daily commisions. You can also earn Fates by ascending characters, and purchase them in Paimon’s Bargains with Starglitter or Stardust, which you get when you wish.
Even with all of that, you might potentially need 80 wishes to get yourself a five-star character. This is why, if you don’t want to spend money, it’s worth saving up your Fates for a character you really want, then going all in to get lucky or hit that 80 wish pity level. That still won’t guarantee you get the five-star you want, but if you’re wishing on a new banner, it will have boosted rates for whoever the featured five-star is.