To enter the Upgrade screen, just tap the Upgrade button on the Hero screen. This will take you to the upgrades available for this Hero.
You can purchase upgrades using the Soulshards. The better the upgrade, the more it costs.
Several skill will be marked with an overload icon, it indicates how many orbs you must place in a row to activate the skill.
Some of the advanced upgrades allow your hero to evolve into a more powerful form.
To do that, you must purchase the earlier upgrades as shown in the picture below.
Thanks to this you can upgrade your existing heroes using extra copies of them.