A. Doing Eruv Tavshilin when the Yom Tov falls on Erev Shabbos:
Whenever Yom Tov falls on Erev Shabbos one must do Eruv Tavshilin on Erev Yom Tov in order to be allowed to cook on Friday for Shabbos.
Cooking on the first day of Yom Tov for Shabbos: When Yom Tov falls on Thursday-Friday it is forbidden to cook foods on the first day of Yom Tov [i.e. Thursday] on behalf of Shabbos even if Eruv Tavshilin was performed. The Eruv Tavshilin only allows one to cook on the second day of Yom Tov [i.e. Friday] on behalf of Shabbos.
Cooking with enough time so the food is ready before Shabbos: Even when Eruv Tavshilin is performed it is only permitted to cook food for Shabbos if there is enough time for the food to be fully cooked and servable to guests on Yom Tov, prior to sunset. It is Biblically forbidden to cook foods if there isn’t enough time left for the food to be served before sunset. Many are unaware of this matter.
The Eruv Tavshilin must be performed on Erev Yom Tov. It may be performed any time on Erev Yom Tov. If one forgot to perform Eruv Tavshilin on Erev Yom Tov then if it is still prior to nightfall [Tzeis Hakochavim] one may still do the Eruv Tavshilin, even if it is already past sunset. If however one remembered only after nightfall then by a regular Yom Tov that falls on Thursday, Friday one may [Bedieved] make an Eruv Tavshilin on Thursday using a Tnaiy that “if today is Yom Tov tomorrow is a weekday etc.” However on Rosh Hashanah one may no longer do the Eruv Tavshilin even through making a Tnaiy. Likewise when any Yom Tov falls on Friday-Shabbos, a Tnaiy does not help.
Reminding the public:
In those years that Eruv Tavshilin must be performed it is proper to place signs by the public areas [i.e. Shul; Mikveh; Website] in order to remind the public of this matter. [It is suggested to also announce this in Shul at the conclusion of Shacharis and prior to Mincha.]
 See Hiskashrus 896
 527/8; M”B 527/3; See Aruch Hashulchan 527/3; Piskeiy Teshuvos 527/3 for other opinions in this matter
 Initially one may not do the Eruv Tavshilin before Erev Yom Tov. [527/2-see there for a dispute on this matter and that initially we are stringent]
 527/9; Biur Halacha 261 “Mearvin”
The reason: As the time of Bein Hashmashos is doubtful whether it is day or night, and since Eruv Tavshilin is a Rabbinical in junction one may be lenient. [Admur ibid]
On R”H one cannot make an Eruv Tavshilin being that it is all considered one long day. [527/22] See Mateh Efraim 581/56
 Aruch Hashulchan 527/14
 Alef Lamagen 581/131