As we wrote above, every year we receive the Torah again.
The Chasam Sofer (Toras Moshe בשבועתיכם ה"ד) teaches that Shavuos is different than all other yomim tovim. "We celebrate Pesach to remind us of what occurred, that Hashem took us out of Mitzrayim. Succos is also to remind us of what was (...דורתיכם ידעו למען). Matan Torah, however, isn't only a memory, but a new reality. Today, we received the Torah from Hashem yisbarach."
Rebbe Moshe Mordechai of Lelov zt'l taught: Shavuos is only one day, unlike Pesach and Succos, which are for seven or eight days. This is an indication of its holiness. All seven and eight days are concentrated into one day of Shavuos.
Reb Eliyah Roth zt'l related that one year, on Shavuos, he was at the Kosel Maaravi with his Rebbe, Reb Shlomke of Zvhil zt'l. Before alos hashachar, his rebbe told him, "Now they are asking in heaven whether we want to receive the Torah. So let's say together Naaseh v'Nishma!" (He explained that Naaseh v'Nishma is in plural, and that's why he wanted to say Naaseh v'Nishma together with him.)
It states (Shemos 20:15) מרחוק ויעמדו וינועו העם וירא, "The people saw and trembled, and they stood from afar." The Divrei Shmuel zt'l explains that the Yidden at Har Sinai saw (through ruach hakodesh) that the future generations will be מרחוק ויעמדו, "standing from afar," which means they will be at very low spiritual levels. Nevertheless, they, too, will accept the Torah. וינעו העם וירא, "The people saw this [the kabbalas haTorah of the future generations] and trembled." They were in awe of the future generation’s devotion to the Torah, even on their low levels.
We say in the brachah on the haftarah, ריקם ישוב לא אחור מדבריך אחד ודבר, "Not one of Your words of the past will return empty." The Aruch HaShulchan (284) explains, "The Torah writes stories that happened years ago, and it sometimes seems that there is no purpose in writing them. But the truth is that what occurred in the past continues to happen in the present. One example is yetzias Mitzrayim. We are obligated to envision ourselves leaving Mitzrayim in every generation. This is because yetzias Mitzrayim continues to happen. Similarly, when Navi tells a story of the past, it continues to occur... This is the segulah of the holy Torah. Therefore, we say, אחור, the episodes of the past, ריקם ישוב לא, don't think they are irrelevant today, because they continue to happen to this day."
The Ruzhiner zt'l wouldn't say divrei Torah on the first night of Shavuos. He explained that the Torah of last year was completed, and the new Torah hadn’t come in yet. He said, "I feel like a farmer before the harvest. The old wheat was consumed, and the new wheat wasn't harvested yet."
The Yid HaKodesh zt'l also didn't say Torah on the first night of Shavuos. He said that this is because דרך לתורה קדמה ארץ, derech eretz is before Torah. "So, what do we do on this night? We prepare for matan Torah with fear of Hashem." After saying this, his limbs trembled from fear (Ramasayim Tzofim, Tana d'Bei Eliyahu 18:56).
The Gemara (Shabbos, end of chapter 18) tells that before the Torah was given on Har Sinai, there was a ruach (spirit) called Tavach (which means Slaughter), which had the power to harm the Jewish nation at that time. Had the Jewish nation not accepted the Torah, this spirit would have slaughtered them and spilled their blood, chas v'shalom.
Therefore, Shulchan Aruch (468:10) states, "The custom is that one doesn't do [the remedy of] blood-letting (דם הקזת) on erev yom tov." We don't want to let out blood at a time when the spirit Tavach is present and tries to cause harm, chalilah.
The question is that the dangerous spirit wanted to harm the Jewish nation three thousand years ago when Hashem gave the Torah on Har Sinai. Why should we worry about it today?
The Machatzis HaShekel answers, "It is known that whatever happened to our forefathers happens again... in the present, when that time arrives."
Reb Shlomo Zalman Auerbach zt'l (Halichos Shlomo, 12:6) quotes this Machatzis HaShekel as an indication that every year on Shavuos, there is a kabbalas haTorah. Shavuos isn’t solely a commemoration of the past; there is matan Torah each year!
We usually don't cut the fingernails and toenails on the same day (see Magen Avraham 260, quoting the Beis Yosef's Magid). The Likutei Maharich (vol.3 p.45, also taught by the Chidushei HaRim zt'l) says that erev Shavuos is an exception. One may cut them both on the same day. He compares this to the halachah of someone with a Torah obligation to go to the mikvah who may cut his toenails and fingernails on the same day, so there shouldn't be a chatzitzah. The Zohar (Emor, written at the end of Tikun Leil Shavuos) explains that the counting of the Omer (which is seven times seven), followed by the tevilah in the mikvah on Shavuos morning, represents purifying oneself to receive the Torah. This tevilah must also be without a chatzitzah. Therefore, one may cut both his finger and toe nails on the same day, on erev Shavuos.