In reading Shabbos 96 today in the ArtScroll edition a lot of the notes and commentary refer to Halacha LeMoshe MiSinai. How is it known what these actually were? It seems that often the Sages will discuss something and then all of a sudden simply say, "Well, that's an Oral Law..." or conversely assert that it isn't an Oral Law.
Are these Halachot actually set out anywhere? How do we know when something was indeed handed down to Moshe at Sinai?
Please forgive us for the delay in responding to your question.
A Halachah l'Moshe m'Sinai has the status of a Torah law (as opposed to a rabbinical law). We only know which law is a Halachah l'Moshe m'Sinai through the oral tradition. G-d told the law to Moshe, Moshe told it to Yehoshua and Aharon and his sons, and it was passed from teacher to student for generations.
Most Halachos l'Moshe m'Sinai became established parts of Jewish lifestyle, so that there is no doubt about their identity as Halachos l'Moshe m'Sinai. However, since these Halachos were passed down through oral tradition and not committed to writing (until the time of the Mishnah and Gemara), the exiles and persecutions that the Jews suffered at the hands of the non-Jews caused breaks and thus discrepancies in the oral tradition, so that it became possible that later generations were not in agreement as to exactly which Halachos were indeed Halachos l'Moshe m'Sinai. At times, when the Amora'im were not sure of the source for a clear Halachah, they stated that it must have been a Halachah l'Moshe m'Sinai, whose identity as such was forgotten. (It is worth mentioning that according to the Rambam, Hil. Mamrim 1:3, it would seem that it has never occurred in history that a Halachah l'Moshe m'Sinai was forgotten. Many Acharonim find that hard to swallow, though, see esp. Teshuvos Chavas Ya'ir #92.)
For further information, I recommend the Rambam's introduction to Mishnayos (available in English, but I don't know offhand the name of the publisher). He discusses your question and enumerates the Halachos l'Moshe m'Sinai. I also recommend Collected Writings of Rav Samson Rafael Hirsch, volume V.