Whenever Young comes in contact with anything harmful (such as enemies or traps), he loses some health.
Health shards may be dropped by all kinds of enemies. 1-health shards can be dropped by small enemies (such as Slimes and Silverfish), and 3-health shards can be dropped by large enemies (such as Slashers and Teleguys).
Activating save points will recover all your health, as long as it wasn't the last save point you used.
At one point, Young may receive a health refill from Finty if they have already acquired the Jump Shoes before they give Finty the Cardboard Box. This is a one-time occurrence and only available in earlier versions of Anodyne.