You gain experience for your Tanks by winning matches. When you have enough experience, an "Upgrade" button will become available and you can spend oil to purchase it.
You can find the upgrade button for each Tank in the Garage while selecting the Tank, or immediately after a Battle during the Victory or Defeat screen. (Given that your tank has enough experience to gain the upgrade).
Alternatively, you can also gain experience in Tanks that are already maxed and transfer that extra experience to other Tanks to help them progress faster by using gems.