When Shabuot begins on Mosa’eh Shabbat, one must ensure not to make preparations on Shabbat for Yom Tob. Since it is forbidden to prepare on Shabbat for after Shabbat, one may not make preparations on Shabbat for the Yom Tob which begins after Shabbat.
For example, one may not set the table for Yom Tob on Shabbat. A woman should wait until Shabbat ends and then recite the Beracha "Ha’mabdil Ben Kodesh Le’kodesh," at which point she lights the Yom Tob candles and may then set the table and make other preparations for Yom Tob.
Likewise, Torah scrolls should not be prepared on Shabbat for Yom Tob. If a Sefer Torah needs to be rolled to the place from where the Torah is read on Shabuot, this should not be done until Mosa’eh Shabbat.
There are, however, a number of exceptions to this rule. Hacham Ovadia Yosef ruled that a person may take a nap on Shabbat so that he will be able to remain awake throughout the night of Shabuot, as long as he does not verbalize that he is going to sleep for this purpose. Since sleep is providing enjoyment on Shabbat itself, it is permissible.
Another example is putting on a special suit on Shabbat afternoon in honor of the Yom Tob. Even though the person’s intention is put on the suit especially for Yom Tob, this is permissible, since wearing the suit also gives honor to Shabbat. One may also immerse in a Mikveh on Shabbat afternoon in honor of the Yom Tob which begins after Shabbat.
It is permissible to remove food from the freezer on Shabbat so it will defrost in time for the Yom Tob meal that night.
One may not ask a non-Jew to perform on Shabbat any act of preparation which is forbidden for a Jew.
Before Shabbat, one must ensure to light a flame that will continue burning throughout Shabuot, in case fire is needed at some point during Yom Tob. One is allowed to light a candle from an existing flame on Yom Tob, but not to kindle a new flame, and therefore one should light before Shabbat a candle that will last through Shabuot so that he is able to light fire when needed. Additionally, one must ensure to prepare before Shabbat enough Halot for Shabbat and Shabuot. Loaves are needed for the three Shabbat meals, and for two meals on each of the two days of Shabuot – a total of seven meals, or fourteen Halot.
Summary: As a general rule, when Yom Tob begins on Mosa’eh Shabbat, it is forbidden on Shabbat to make preparations for Yom Tob, or to ask a non-Jew to make preparations. However, one may take a nap on Shabbat to prepare for remaining awake throughout the night of Shabuot, as long as he does not say that this is his reason for napping. One may put on special clothes for Shabuot on Shabbat afternoon, and immerse in the Mikveh, and one may take out of the freezer on Shabbat food that is needed for Shabbat.