The situation of Erev Pesah occurring on Shabbat affects a number of different aspects of the pre-Pesah schedule. These changes begin with the observance of Shabbat Hagadol (literally, "the Great Shabbat"), which we normally observe on the Shabbat immediately preceding Pesah. Several different customs are practiced on this Shabbat, most notably the "Derasha" (lecture) delivered by the Rabbi of every community consisting of insights into the Haggada and practical instruction concerning the Pesah celebration. When the Shabbat immediately preceding Pesah is Erev Pesah, delivering the Derasha on this day obviously does not allow the congregation time to apply the material as they make their Pesah preparations. Hence, it is customary on such years to observe Shabbat Hagadol a week earlier, so that the people will learn the relevant material while there is still time to implement it.
Generally, the day of Erev Pesah is also observed as "Ta'anit Bechorim" the Fast of the Firstborn. All firstborn males are required on this day to either fast or to absolve themselves of fasting by participating in a "Se'udat Misva" (meal involving a Misva), such as a Siyum (completion of a Talmudic tractate). When Erev Pesah occurs on Shabbat, of course, the fast cannot be held on Erev Pesah. Some communities observe Ta'anit Bechorim on Friday in such a case, whereas others including our community observe Ta'anit Bechorim on Thursday. (The Steipler Gaon reportedly observed Ta'anit Bechorim on both Thursday and Friday in this case.) Therefore, when Erev Pesach occurs on Shabbat, firstborns must make a point of participating in a Siyum on the previous Thursday in order to absolve themselves of the obligation to fast.
Bedikat Hames (the search for Hames) normally takes place on the night before Erev Pesah. When Erev Pesah falls on Shabbat, however, the Bedika is performed on Thursday night. One follows the same procedure for Bedikat Hames as in regular years, including the recitation of the Beracha. Bi'ur Hames (the burning of the Hames), which is normally performed on the morning of Erev Pesah, is, in a case where Erev Pesah falls on Shabbat, performed on Friday morning. In such a situation, however, one omits the "Kal Hamira" declaration which is normally recited when burning the Hames, whereby one renounces ownership over any remaining Hames. Since one will still eat Hames on Friday and Shabbat morning, one cannot renounce his ownership over his Hames at this point. This declaration is therefore made only on Shabbat morning, after one has eaten all the Hames he plans to eat before Hames becomes forbidden.