You can view a character's talents by going to the character screen, and selecting the talent's tab. This screen shows all their skills, including their normal attacks, charged attacks, elemental skill, elemental burst, as well as their passive.
It also displays in depth details like the numbers of their damage multipliers, cooldown time of your skills, energy requirement, etc. Leveling these up is quite important since it does affect your skills, and some of them can give a decent increase per level.
How to unlock and level up talents
In order to level up your talents, you need to ascend your characters. After that, you still need to get some materials for it too.
You can find materials used for ascension, and items like talent leveling by going to domains. You can view these by going to Adventurer Handbook and selecting the "Domain" section. You will need to unlock them though. The rewards from the domains are tied to certain days.
When viewing the domains, you can tap the "?" icon on the right, and see what drops which item on a specific day. If you miss it, you will have to wait until it arrives again.