From the Heroes menu, tap on the hero you want to upgrade, then select Skills. You can see the skills you've unlocked for that hero, based on their Grade level.

Your Skill Level for a particular skill can only go as high as your Hero Level. Raise your Hero Level to raise the threshold your Skill upgrades can reach.

Also note that you can only upgrade so many Skills before you need to recharge your Skill Points. All skill upgrades require bucks and Skill Points to unlock.