The DC of the saving throw is based on the caster: 8 + proficiency bonus + casting ability modifier. (PHB p.205: "Saving Throws")
The GM rolls a d20 on behalf of the monster, adds the appropriate saving modifier based on the monster's stats, and compares to the spellcaster's save DC.
Your specific questions:
What are "any special modifiers?"
Things other than your ability score or proficiency that explicitly modify your saving throw. For instance, a Cloak of Protection will grant you +1 on all saving throws. (DMG p.159)
Is this example correct?
To complete the example, if the monster was a Revenant, CR 5 would mean +3 proficiency so would add 3 to the d20 roll.
This is true if and only if the Revenant is proficient in the implicated save. If you look at the stat block for a Revenant (MM p.259) you'll see saving throw modifiers listed for STR, CON, WIS, and CHA. You'll also see that the modifiers there are all three higher than the associated ability modifier. That's the proficiency/CR bonus, worked right into the stat block. (DEX and INT would save just as those ability modifiers.)
A worked example:
Your 6th-level, 16-WIS cleric Clare-Bear casts Sacred Flame at the zombie ZomTom. The description of Sacred Flame allows for a Dexterity save. (PHB p.272)
At 6th-level Clare-Bear's proficiency bonus is +3. With 16 WIS her spellcasting ability modifier is +3. Thus her save DC = 8 + 3 + 3 = 14.
ZomTom's DEX is 6, for a -2 modifier. He is not proficient in Dexterity saves. So ZomTom gets a net -2 modifier to its saving throw. (PHB p.311.)
So if the GM rolls a 16 or higher, achieving a 14 or higher after ZomTom's -2 DEX mod, he will have succeeded in his saving throw. (Ties always go to the roller of the d20; see PHB p.7, "The d20".)
 Note that any proficiency bonus that the creature would gain from its challenge rating is already factored into the stat block. See, for instance, the Young Bronze Dragon on MM 108, whose CHA mod and CHA saving mod do not match. The dragon's proficiency bonus is added to the CHA mod as per "Proficiency Bonus by Challenge Rating" found on MM p.8. If there is no mention of an ability under "Saving Throws" then the creature is not proficient in that save.