Depends on the overlap. If it's for every note or two, or instead, for one passage to the next. Think of it as breathing on the pedal with your foot in the first case and lightly at that. In the later instance I look at that the other way around, when to let off the pedal. Either way generally has a pulse and becomes a kind of pumping action onto or off of the pedal. In time it becomes automatic.
On acoustic pianos I use a very light foot on the pedal, I don't depress it very far. On my digital I usually cram it to the floor if there is a lot of pedal in the piece. Two completely different approaches. My grand would ring into the next county if I used the pedal like I do on the digital.
Ranniks mentioned Fur Elise. Fur Elise is the very first piece I learned to feather the pedal on, ever so slight brief touches of pedal, almost non existent. From there I learned to adjust pedal usage for certain passages. I used the most on the cascading/decending scale near the end but, I believe, even then it was not full pedal I used.