When one completes Bedikat Hames (the search for Hames conducted on the night before Erev Pesah), he must recite the text of "Bittul Hames" – the renunciation of ownership over Hames. This declaration, which is customarily recited in Aramaic ("Kol Hamira Va'hami'a De'ika Be'reshuti…"), means, "All Hames and leavening agents that are in my possession that I did not see and did not burn are hereby nullified and should be like the dust of the earth." One must recite this declaration given the possibility that there is some Hames in his possession that he did not discover during his search. In order to avoid violating the prohibition against owning Hames during Pesah, one must recite the "Bittul" and renounce ownership over any remaining Hames.
One must recite this declaration in a language he understands. Thus, the Aramaic text should be recited only if the individual understands the words. If he does not understand the Aramaic, he must recite it in a different language, which he understands. (Interestingly, the Talmud Yerushalmi, which was composed in Eres Yisrael, presents a Hebrew text of the Bittul declaration, as opposed to Aramaic.) If one did not understand the text he recited, the Bittul is not valid and must be repeated in a language the person understands.
The declaration should be recited three times, and in one of the three times the person should add the word "Ke'hefker" in the final clause – "Lihavei Hefker Ke'afra De'ar'a" ("It should be ownerless like the dust of the earth").
Hacham Ovadia Yosef writes that if a person appoints somebody else to search his home on his behalf, the homeowner should nevertheless recite the Bittul declaration. Even though he does not personally perform the Bedika (search), it is still his responsibility to recite the Bittul. It should be noted that one can recite the Bittul wherever he is; even if he is far away from home, he may (and must) still declare the Bittul in order to renounce his ownership over the Hames.
If a person is away and his wife suspects that he may not remember to declare the Bittul, she may recite the declaration on his behalf, even though he did not commission her to do so. In such a case, she recites, "Kol Hamira…De'ika Be'reshut Ba'ali…" ("All Hames…that is in my husband's possession…").
After one completes the search and recites the Bittul, he should store in a safe place all the Hames that he will eat or burn the following morning. It should be kept somewhere high, out of the reach of children, and should be covered, such that rodents cannot access it, in order to ensure that it will not be spread around the home.
On the morning of Erev Pesah, of course, one may eat as much of the Hames as he wishes, and the rest must be destroyed.