There are different currencies in the game that you should know about. If you have completed the tutorial, you should already see there at the top left 3000 free experience.
Free experience: You can get this free experience (blue) by playing matches or by converting unit experience using the premium currency gold (not recommended). You need free experience first and foremost, to unlock new commanders. You can also use this to upgrade your commander to the next level or buy your troop equipment with it (If at all recommended only in the high tier)
Gold: In addition to free experience, there is also gold, which you can buy with real money, but you don't have to (see 8. and 9.). If you play actively and regularly, you will automatically receive gold over time through the level-up system and can use it to unlock premium time. (A guide to this is yet to come)
Premium Time: Premium time makes your life easier. If you play with Premium, you get: +50% Free Experience, +50% Unit Experience, +50% Silver, 1 Premium Slot for the Daily Missions, a few Commander Tokens and... ... every player in your team who owns Premium ensures that there are +1% more rewards at the end. (All players with Premium = +10% reward)
Commander Tokens: If you buy gold, you will also receive "Commander Tokens", with these you can test a commander that you don't own for 1 hour.
Silver: You need silver for so-called "consumables" with which you can temporarily improve some of your troops' statistics.
Unit Experience: Finally, of course, there is the unit experience (green), which you cannot see in the photo at the moment. This is tied to a unit and you need it to improve your troop gear and unlock new units. (See 5.)