How do I increase skill levels of heroes?

Go to the hero menu (icon on the lower right) and find the heroes that you have recruited / stationed. Tap on the required hero to view it and then sap the book style icon to the lower right. Here you will see their skills. You can tap on any to view the details and upgrade it, you will need to spend wisdom medals to do this.

Only the first skill will be unlocked initially, the others will need to be unlocked. You may need to reach higher Exp levels and use wisdom medals, money and hero medals up unlock the others.