The Uthgardt Shaman (in the Storm King's Thunder adventure) has an "Innate Spellcasting" ability, which among other things lets her cast the Prayer of Healing spell once per day. That spell includes the creature's "spellcasting ability modifier" in the amount of hit points to heal. But I can't find anywhere that says what that ability modifier would be. How do I know which ability modifier is being referred to when a creature uses its Innate Spellcasting?

It is normally written in the stat block.

The Uthgardt Shaman's Spellcasting Ability is Wisdom.

For example, you can see that Djinni has innate spellcasting as well. The spellcasting ability and other relevant information (DC, bonus to hit) are written before the list of spells available.

The spellcasting ability information is missing in the Uthgardt Shaman's stat block but the +4 bonus to hit (or 12 spell save DC) can give you the required information. Looking at the skills, the Shaman has a +2 proficiency bonus. Reversing the calculation for spell hit bonus will show their spellcasting ability modifier: +4 to hit with spell attacks equaling +2 proficiency and +2 spellcasting ability modifier.

If there was only the spell save DC the logic would be the same. DC calculation for spells is 8+proficiency+ability. Reversing the 12 DC from Shaman's stat block you get: 8+2(proficiency)+2(ability modifier)

You can also confirm a monster's proficiency bonus on the Proficiency Bonus by Challenge Rating table in the DMG p.274.