From the [Wiki](http://starbound.gamepedia.com/Health):
> Using a Bandage, Medkit, or Red Stim Pack.    
Sleeping in any Bed, tent or any object it is possible to sleep on.   
Eating certain foods can temporary increase health regeneration.    

For foods that heal, see [this question](http://gaming.stackexchange.com/questions/146972/which-food-items-heal-you-and-by-how-much).

Beds are easy to craft and you can find tents and sacrificial altars, both of which act like beds while exploring.