For upgrading a unit, you need to choose an existing one and select the level and method of upgrade. You can use Instant upgrade which costs Silver. Taking Swordsman as an example,
 
Select an existing unit and choose the level to be upgraded to, as well as how to upgrade, as shown below:
Click the cross-swords icon in mini menu pop-up:
 
Players can upgrade a unit by 2 levels at once or up to level 5, what ever is higher. Exception: With high VIP-Rank up to 4 Upgrades are possible.