Beginning from thirty days before Pesach, the Mitzvah of eliminating Chametz takes effect. This includes all of the Pesach cleaning and all measures taken to ensure one does not transgress the prohibition of consuming or owning Chametz on Pesach.
It is therefore incumbent on each of us to begin to take heed that any food products one plans on using on Pesach not come in contact with Chametz. Similarly, shop-keepers and store-owners must make sure to place kosher for Pesach food items in clean places so that they do not come into contact with Chametz, such as flour and the like.
The basis for this law is from the Gemara (Pesachim 6a) which states that if one sets sail thirty days before Pesach, one is obligated to eliminate all Chametz in one’s possession before departing. The Rishonim derive from here that the Mitzvah of eliminating Chametz begins thirty days before Pesach and continues until the time Chametz is burned on Erev Pesach. (If, G-d-forbid, one finds Chametz later than this time, one must likewise eliminate it immediately.)
In previous generations, food products were generally made from basic, raw ingredients, such as fruits, vegetables, legumes, and the like. In the past several generations, however, where the food service market has been largely commercialized and subjected to many technological advancements, it has become necessary to appoint Kashrut supervisors for Pesach and year-round. Thus, nowadays, food products acceptable for Pesach use must be marked with a “Kosher for Passover” denomination.
All loose food products that could conceivably contain Chametz, such as dried fruits, nuts, seeds, cheeses, and the like may not be purchased for Pesach unless the shop-keeper is a G-d-fearing individual who knows all of the ingredients these Pesach-sensitive items contain (it is sometimes difficult to ascertain all of the ingredients in some products, like cheeses), in which case one may rely on his word that these foods are kosher for Pesach. However, one may not rely on the word of shop-keeper who is not G-d-fearing regarding the Kashrut of food products.
Thus, if a shop-keeper is non-religious or non-Jewish (applicable to many supermarket chains in Israel and abroad), one may not purchase food products for Pesach from such an establishment, unless it is a sealed product with a reliable “Kosher for Passover” symbol.
Maran Ha’Chida writes in his Sefer Avodat Ha’Kodesh (Section 196) in the name of our Sages that anyone who is careful not to transgress the prohibition of consuming or owning Chametz on Pesach even in the slightest is guaranteed to have a good year, for the Pesach holiday is the source of the rest of the year.