One may not prepare from Yom Tov to Shabbat unless one does Eruv Tavshilin before Yom Tov.
Since the first day of Shavu'oth is on Friday, everybody needs to do Eruv Tavshilin on Thursday. 
 One takes a Challa one is going to use on Shabbat and a cooked food that will be eaten on Shabbat and one says the Bracha:
 בָּרוּךְ אַתָּה ה' אֱלקֵינוּ מֶלֶךְ הָעוֹלָם
אֲשֶׁר קִדְּשָׁנו בְּמִצְוֹתָיו
וְצִוָּנוּ עַל מִצְוַת עֵרוּב 
 One continues with the following, which must be said in a language one understands:
 בַּהֲדֵין עֵרוּבָא
 יְהֵא שָׁרֵא לָנָא 
 לַאֲפוּיֵי, וּלְבַשּׁוּלֵי,
 וּלְאַטְמוּנֵי, וּלְאַדְלוּקֵי שְׁרָגָא, 
 וּלִמֶעְבֵּד כָּל צָרְכָּנָא 
 מִיּוֹמָא טָבָא לְשַׁבְּתָא 
 "With this Eruv
 we are permitted
 to bake, cook,
 keep things warm and light fire
 and do all that is needed
 from Yom Tov to Shabbat".
 The Challa and food should be kept in a safe place; if they are eaten before Shabbat, a Rabbi should be consulted how to proceed.
 Even those who don't have to cook for Shabbat, still need to do Eruv Tavshilin in order to light Shabbat candles (from an existing flame.)
 Source: Kitzur Shulchan Aruch 102
 - Danny 
 Wednesday, 4 Sivan 5769, 48th day of the Omer