You can run the game just fine without ever using a modified skill; if I remember right, they got rid of those rules in a later version of Fate and few people cared.
Still, it's a good option to have for ambiguous cases. A while ago I had a player flying very fast when a cage was conjured around them; I wasn't sure whether Athletics or Alertness was the most appropriate defence skill, so I had them roll Athletics modified by Alertness.
Anyway, there are three skills for which the corebook offers modification-specific stunts/Powers. Might, Discipline, and Endurance. Not coincidentally, those are the three skills most likely to modify another. Might for any physical action you take while weighed down, Discipline for any challenge that's at least partially about keeping your cool, and Endurance for anything you do continuously for a long time or while very tired.
As I recall, the corebook says long-distance running uses Athletics modified by Endurance.