There are two types of currency in Riders Republic and they are both used for cosmetics, emotes, and other gear. These are Republic Bucks and Republic Coins and you'll need them to customize your look.
Republic Coins are the premium currency for the game and thus must be purchased with real money. Some items can only be purchased with these while others can be purchased with Bucks or Coins.
Republic Bucks are the in-game currency and are earned as you play by completing activities. Completing races and events will earn Bucks and are one of the main ways to collect them. You can also earn Bucks by gaining sponsors and completing sponsor events. You can only earn Bucks by completing an event the first time.
Ranking up will also reward you with Bucks. So by doing better and completing the event challenges you can rank up and earn more money. There are also collectibles scattered across the map that will give you a few Bucks. These are RR Balloons and they are worth 50 Bucks each. While this isn't a lot, there are 500 of them so it is worth it to grab them when you spot them.