I have heard that willpower is finite and every person starts their day with a limited capacity.
On the other hand there are people like gym goers or sportspersons saying that they can muster up more will power if they have the right mentality at the right time.
I don't know which one is right, but is it possible to increase one's capacity for will power ? If so what kind of exercises or training methods do they have to use ?
What you are citing, that willpower is being used up over the day by decisions, is called ego depletion and it is wrong! There are experiments where two groups were either told that this is a thing or the opposite, that willpower is strengthened by every decision instead, and it turns out, that both groups had different willpower self assessments at the end of the trial in accordance with the theory of willpower they were told in the beginning, meaning it's just a placebo in the end.
Neither ego depletion nor the opposite exist, but people feel as strong in willpower in accordance with their belief of how willpower works.