On this page of the Tunic guide, you will learn how to recover Health Points in several different ways.
Using magic potions
The main way to restore health in Tunic is to drink magic potions. However, you start the game without a single drink. Where to find them? In treasure chests and stores - in some, you will find full bottles; in others, you will find pieces of them (three will make one whole potion). After obtaining them, you can use them until stocks run out. After using magic potions, you don't need to look for new bottles - just go to any shrine (checkpoint), and all potions will be refilled again. Also, remember that the effect of healing using magic potions can be increased by investing in corresponding stat points. You can find more about this tipic on the page: Character development.
Healing at shrines
You will restore your health to the full each time you visit any shrine (checkpoint). Just like that. Where's the catch? Interacting with the checkpoint also respawns all enemies you defeated (except the bosses). So you will recover HP, but at the same time, you will have to face the enemies once again.
You will recover a small percentage of health by using red fruit, which is one of the basic consumable items. You can find it in treasure chests and purchase it at stores.
The last, and the least common way to heal the character in Tunic, is to collect hearts that drop from enemies. However, to have a chance for them to appear after defeating an opponent, you must have a Lucky Cup card equipped. You will find it south of the red mill in Overworld, almost in front of the Envoy guarding the passage to the key. Don't know what we're talking about? Then check out the page: Shield - how to find it? and you certainly won't have any problems finding the mentioned card.