How do I heal without potions?

You can only heal by using potions or resting at, fast travelling to or setting up an Inquisition camp. They are marked as tents on your map. Going back to Haven/Skyhold will also heal you.

There are no healing spells for any mage in the game. The closest thing to a healing spell is the Revival spell from the Spirit magic branch, which will revive fallen allies.

You replenish your stock of potions when you rest at, fast travel to or set up an Inquisition camp. Some levels contain Supply Caches which will also replenish your potions. Going back to Have/Skyhold will also replenish those. You can increase the number of potions you can carry with you by getting the "More Healing Potions" Perk in the Forces section. That will permanently increase the number of healing potions you can carry up to 12. You will need to have already spent 3 perks in the Forces category to be able to buy it.

There is also a grenade that can heal you. Healing mist will create a cloud that will heal a small amount of health of any allies within it. Each party member can carry up to 3 of those. As other grenades, these won't replenish automatically when you rest or go to Haven/Skyhold. You will need to fill them up at Potions Stations for one spindleweed each at the base level, and one spindleweed and one embrium at the upgraded level.

People often forget there is a passive healing effect they added into the game: the heal on kill passive. This is an effect that can be found on rings, belts, and amulets or from certain cloths when used in an offensive slot. Keep in mind, however, that the character with this equipped has to literally get the kill, meaning only one character can heal off of a given enemy's demise. That being said, when a kill generates up to 27% of your health bar, you can afford to share the wealth. Noted, this doesn't help with boss fights, but you can heal up afterwards by hunting small animals like rams or foxes.

There is only one healing skill in the game (healing as we usually understand it).

That is the "Resurgence" from Knight-Enchanter tree.

Description below:

You call on benign spirits to restore you and your allies for continuing the fight. All party members are healed to full health, including those who have fallen unconscious, and a glyph around you provides ongoing healing to the party for the spell’s duration.