Let's take this stat block as an example. It says the creature has +2 DEX and +6 Stealth. Does the Stealth bonus already include the ability modifier, making a stealth check for this creature essentially a 1D20 + 6? Or would it be 1D20 + 8 because of the +2 DEX?
Skill bonuses are already baked into the stat blocks.
From the intro to the Monster Manual:
The Skills entry is reserved for monsters that are proficient in one or more skills. For example, a monster that is very perceptive and stealthy might have bonuses to Wisdom (Perception) and Dexterity (Stealth) checks.
A skill bonus is the sum of a monster’s relevant ability modifier and its proficiency bonus, which is determined by the monster’s challenge rating (as shown in the Proficiency Bonus by Challenge Rating table). Other modifiers might apply. For instance, a monster might have a larger-than-expected bonus (usually double its proficiency bonus) to account for its heightened expertise.
If the monster has proficiency in a particular skill, the total bonus to that check will be printed on the stat block. If it does not have proficiency, you just add the relevant ability modifier to the d20 result.