Immediately at Tzet Ha'kochavim on the night before Erev Pesach (Mishna Berura 431:1); this occurs (in the New York City area) approximately 40 minutes after sundown. If one performed the Bedika earlier than Tzet Ha'kochavim, he has nevertheless fulfilled his obligation, though he should preferably conduct another search after nightfall (Halichot Olam).
The Mishna Berura (431:7) cites a dispute among the authorities in this regard. One view allows one to begin studying Torah during this period, but the Mishna Berura clarifies that this does not refer to intense, in-depth study, which might cause one to forget to perform Bedikat Chametz. The other view forbids beginning a study session after Tzet Ha'kochavim unless somebody will remind him to perform the Bedika, or if he learns in a group who will remind each other after the session to perform the Bedika.
Chacham Ovadia Yosef, in Halichot Olam, rules that if delaying the class will not affect attendance, and all participants will be able to attend at the later time, then the class should preferably be delayed. Otherwise, it may be held at its regular time, before Bedikat Chametz, and an announcement should be made after the class reminding the participants to perform the Bedika immediately upon returning home.
The Mishna Berura (431:8) rules that if one regularly prays Arvit with a Minyan in the synagogue at Tzet Ha'kochavim, he should do so even on the night of Bedikat Chametz and perform the Bedika afterward. And if this night he happens to pray privately, at home, he should preferably appoint somebody to begin the Bedika on his behalf as he prays Arvit at Tzet Ha'kochavim; if nobody else is available, then he should first recite Arvit and then perform the Bedika. However, a person who normally recites Arvit privately at home should first conduct Bedikat Chametz and only then recite Arvit. According to other views, even such an individual should first recite Arvit before performing the Bedika.
The Shulchan Aruch (431:2) rules that so long as one had begun the activity during the daytime on the thirteenth of Nissan, he may continue even after Tzet Ha'kochavim and perform the Bedika when he finishes the given activity. The Rama (431:2), however, requires that one interrupt his activity at Tzet Ha'kochavim, since this is the optimal time for the Bedika.