1. One who discovers chametz in his home during Pesach — if he found it during Chol HaMoed(the intermediate days of the festival), he should immediately remove it from his domain and burn it. But if he found it during Yom Tov (the [Sabbath-like] first and last days of the festival), he should not burn it [since this would be kindling that is not needed for the festival], nor should he even remove it from his domain [since the chametz is muktzah]. Rather, he should cover it with some utensil so that he not come to eat it. At night, after the conclusion of Yom Tov, he should burn it (Shulchan Aruch and Mishnah Berurah 446).
2. If there is non-Jew present, one may tell him to throw away the chametzto waste, even if it is chametz that had been nullified prior to the festival. However, the custom is to not do this but rather to cover it with a vessel (Mishnah Berurah ibid.).
