There are 3 different currencies in the game: Gold, Gems, and Crystal Coins.
Gold is the main currency that you get from playing the game, and it's used to purchase Mini Fragments in the shop.
Gems are a premium currency that's used to buy Hero shards and Mini skins.
Crystal Coins are used to buy some of the more unique skins in the game, like the Party Wizard or Squitch.
How to Obtain/Farm
Aside from playing some games, the easiest and most reliable way of getting some gold is by doing quests.
There are daily, weekly, and Mini quests that you can do for various rewards, but many of them always include some gold or carrots.
Carrots are used to progress the season rewards. You can get various rewards like Hero or Mini Fragments, but there are also some gold here and there.
If you are a paying player, you can purchase Gems and convert them to Gold.
Gems are mainly obtainable by purchasing them in-game with real money. New players are given 100 gems when they first start playing the game. After that, you can get 10 more every time you level up.
The only other way to reliably get gems without using real money is to win raids. This is a PvE content that you can do when you are in a clan. Raid bosses can only be spawned every 2 days, so you can only get 5 gems every 2 days.
Crystal Coin is obtainable when you get more copies of a Mini or Hero when you already have them maxed.
Best Use of Items
In the shop, you can buy Mini Fragments with Gold.
2 Elixir Minis costs 250.
3 Elixir Minis costs 500.
4 Elixir Minis cost 750.
There are 6 options, and they change daily, but you can also refresh the list up to 10 times daily with the button on the upper right. The first time is free, but they cost more and more gold with each reset.
Early on, it's best to purchase new Minis since this will unlock new quests for them so that you can get more carrots, which will help with the season's rewards.
In the shop, Gems are mostly to buy Hero Fragments or convert to Gold. You can buy new Heroes to try them out, but if you want to be careful with your gems, then it's recommended to buy Fragments for a Hero that you already have to increase their level and unlock new abilities.