Common exercises which generally require a spot during core muscle training with heavy weight are free weight bench press, and free weight squats. Though any exercise can utilize the added core muscle training and building benefit of a good spot, these are the two big dogs that require a spotter when using heavy weight.

Procedure for a spot during core muscle training:

The spotter will generally only slightly assist the lifter in the reps where he begins to show signs of struggle. Then the spotter will increase his assistance until the trainee is clearly no longer able to perform another rep, at the completion of the previous rep. Here the spotter assists the trainee in racking the weight, thus completing his core muscle training set.

The universal problem: the "jackass spotter":

Unfortunately there are no "schools for spotters" in the typical gym. If there were perhaps there would be less of what we coin as, "the jackass spotter". This is the type of spotter who will practically lift the bar with all his might from the onset of the exercise. He will not even wait until you need the spot, he will begin assisting you from the get go with all his might, successfully negating any muscle building effect from your core muscle training.