When the 14th of Nisan coincides with Shabbat, bedikat ḥametz is performed with a berakha on the night of the 13th, Thursday night, because it is impossible to seek and eliminate ḥametz on Shabbat. After the search, the ḥametz is nullified like in any other year, and on the following day, Friday, it is burned. It is best to burn it by the sixth seasonal hour of the day so that no one gets mixed up on other years (SA 444:1-2). Ḥametz that will be eaten during the first two Shabbat meals is carefully set aside.
If it were permissible to eat matza on Erev Pesaḥ, we would presumably use matza at our Shabbat meals in order to avoid the problem of ḥametz. However, since it is forbidden to eat matza on Erev Pesaḥ so that it is appetizing to us at the Seder (see above, 13:6), we must save ḥametz for the first two Shabbat meals. In order to avoid problems with ḥametz foods, many people cook kosher-for-Pesaḥ foods for that Shabbat. They make kiddush and eat bread with spreads or salads in a room where people will not eat during Pesaḥ. After eating bread, they clean their hands and brush off their clothes, then eat the rest of the meal in the kosher-for-Pesaḥ dining room.
The first Shabbat meal is eaten on Friday night, and the second on Shabbat morning. It must be completed by the end of the fourth seasonal hour, at which time ḥametz becomes forbidden (as printed in many calendars; see above, 3:6). Shabbat morning prayers must begin and end early so that the meal can be completed in time.
After the second meal, all remaining ḥametz must be gathered from the plates and tablecloth. Since it may not be burned on Shabbat, it is a good idea to flush it down the toilet and thus completely destroy it. People generally plan their Shabbat meals wisely, so that it will be easy to gather up the leftover ḥametz and dispose of it. After this, the ḥametz must be nullified; the bitul must be recited by the end of the fifth hour of the day. After the meal, one should brush his teeth well (above, 11:12).
Se’uda shlishit, the third Shabbat meal, presents a problem: It is forbidden to eat ḥametz after the fourth hour of the day, and matza is forbidden the entire day. As a result, the obligation to eat a third meal is met by eating meat and fish or various fruits (SA 444:1). One may also eat matza balls, and according to many authorities, one may eat whole matzot that have been thoroughly cooked. One must avoid eating excessively during the third meal so that the matza of Seder night remains appetizing. There are other suggestions for those who wish to destroy all of their ḥametz before Shabbat, as explained in the notes.
Cooked matza: Another option is to cook a whole matza. According to most opinions, one may eat cooked matza on Erev Pesaḥ, since it has been fundamentally altered and one would not fulfill the mitzva of eating matza on Seder night with such matza. Because it constitutes at least a kezayit, its berakhot are still “ha-motzi” and “Birkat Ha-mazon” and consequently one may use it to fulfill the obligation to eat three Shabbat meals. This is the ruling of MB 471:20 and SHT 19 ad loc., AHS 444:5, and Yeḥaveh Da’at 1:91 n. 10. SHT 471:20 mentions in the name of SAH and Ḥayei Adam that frying is the same as cooking, and that Pri Megadim equivocates. On the other hand, MA 444:2 says in Maharil’s name that he never saw anyone adopt the practice of eating cooked matza at se’uda shlishit, and Gra implies that it may not be eaten on Erev Pesaḥ. Those who wish to follow the majority ruling and fulfill their obligation with cooked matza may do so (see SHT 444:1 and above 13:7). MB 444:8 raises the idea of splitting the second meal into two, but this is not ideal, as se’uda shlishit should be eaten after midday (SA 291:2; Peninei Halakha: Shabbat 7:2).