When Yom Tov falls on Friday, Halacha forbids cooking or making any preparations on that day for Shabbat, unless one follows the procedure known as "Eruv Tavshilin." The Eruv Tavshilin is made on Erev Yom Tov; thus, if Yom Tov falls on Friday and Shabbat, one would make the Eruv Tavshilin on Thursday, before the onset of Yom Tov. One takes a Ke'zayit (the volume of an olive) of bread or, on Pesach, Matza together with a cooked food our practice is to use an egg and sets them aside. He then makes the formal declaration stating that through this Eruv it will be permitted to cook, bake and make any preparations necessary on Yom Tov for Shabbat. Without making an Eruv Tavshilin, one may not prepare on Yom Tov for Shabbat.
Hacham Ovadia Yosef ZT"L writes that even if one did make an Eruv Tavshilin, he should preferably not cook and prepare for Shabbat late in the day on Yom Tov, shortly before the onset of Shabbat. He should endeavor to prepare the food early enough in the day that it could potentially be served to guests who arrive while it is still Yom Tov, before Shabbat. This is an additional measure of stringency; if one cooked food late in the day on Yom Tov, the food is nevertheless permissible for consumption on Shabbat. Preferably, however, one should prepare food earlier in the day.
Summary: When Yom Tov falls on Shabbat, one must make an Eruv Tavshilin on Erev Yom Tov to allow preparing on Yom Tov for Shabbat. Even if one did make an Eruv Tavshilin, he should preferably not prepare food for Shabbat late in the day on Friday.
