The basic PHB rule: Without healing, a character on 0hp must be stabilized by applying first aid, requiring a DC10 WIS: medicine check.
The campaign extension of that rule: “first aid” is not something everyone knows. Proficiency with a healers kit or medicine confers advantage. In a combat situation, disadvantage may also be experienced.
Situation-dependent: a 20 confers 1hp as well as stabilizing while a 1 means a failed death roll.
As an alternative to this campaign extension, if you have a particular combat feature that might stand in for cool-headedness when life is in the balance (such as Warcaster) you may choose a two-step, Concentration then Medicine approach, neither at disadvantage from this particular situation.
Potions for unconscious characters
Proficiency in either healers kit or medicine are required to administer a potion as it is intended, to an unconscious ally.
Without such proficiency a disadvantage DC10 WIS check (not save) is required. A 1 means a failed death roll.
Administering a potion as an embrocation
Some potions may, dependent upon source and patient, offer a lesser effect when poured on. Here is a quick summary:
Goodberry: N/A but is simpler to administer without choking the patient – a DC10 WIS: medicine check provides the intended 1hp as the patient’s saliva draws the effect into the body’s own healing system
Basic 2d4 healing: 1hp
Cure wounds 1d8+potion creator’s spellcasting modifier: 2d4
Higher levels: each extra “d8” the potion is imbued with allows a d4 to be added to the “pour on” effect.
General principle of other healing spell potions: Potions created above the minimum 2d4 effect can be simply poured onto bare skin. They have the next level down in effect. Note that Healing spirit (XGTE) works exactly like a paladin list Aura of Vitality.