There is a time-honored tradition to remain awake throughout the night of Shabuot and read the special "Tikkun Lel Shabuot" text that is printed in the Mahzorim. Hacham Ben Sion Abba Shaul (Israel, 1924-1998), in his work Or Le'siyon (vol. 3, 18:11), discusses the importance of this custom and presents numerous laws and guidelines relevant to the proper observance of this special occasion (listen to audio clip for precise citation).
First, he mentions that even learned men who prefer studying Gemara must set aside their Talmudic studies in order to read the text of the Tikkun Lel Shabuot. If time remains after they complete the Tikkun, they may then study other material that they find more enjoyable. In Yeshivot, Hacham Ben Sion writes, students should follow the instructions of their Rosh Yeshiva in this regard.
He also emphasizes that one should read the Tikkun even if he does not understand some sections of the service.
Even if one plans to remain awake throughout the night, he should nevertheless recite the Keri'at Shema Al Ha'mita before Hassot (midnight as defined by Halacha). Already after Hassot, one may recite all the morning Berachot, with the exception of "Al Netilat Yadayim" and Birkot Ha'Torah. One should make a point to use the bathroom at some point before morning in order to be able to recite "Asher Yasar."
At the point in the pre-dawn hours when it is uncertain whether Alot Ha'shahar (daybreak, the first appearance of light in the eastern sky) has occurred, one should discontinue his Torah learning. He should instead either immerse in a Mikveh or sing songs of praise until Alot Ha'shahar.
After Alot Ha'shahar, one should wash his hands in preparation for prayer, but without reciting a Beracha. He then must recite Birkat HaTorah.
Hacham Ben Sion cites in this context a passage in the work Sha'ar Ha'kavanot, which comments that whoever remains awake and diligently involves himself in Torah study throughout this night is guaranteed to survive the entire next year and to avoid all harm. Nevertheless, one should make a point of studying "Li'shmah" with the proper motivation, out of sincere love for and commitment to Torah learning, and not to receive reward. Hacham Ben Sion also warns that sitting idly or engaging in meaningless chatter is no better than sleeping. It is therefore imperative to ensure to spend the entire night engrossed in Torah learning, and not in any other activities. In particular, one must avoid idle conversation inside the synagogue. Hacham Ben Sion also cites a comment from the Zohar that emphasizes the importance of studying with joy and fervor, in reward for which one is blessed with seventy blessings. The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909) similarly stressed the importance of studying on this night with great enthusiasm and what he termed "purity of heart."
Furthermore, on the festival of Shabuot God decrees how many "Hiddushim" (new insights) each individual will be privileged to develop during the coming year, which is determined based on the level of one's intensive study on Shabuot. Hacham Ben Sion writes that when we speak of Shabuot as "the day of the giving of the Torah," we refer not merely to the historical event of Matan Torah, but rather of the process that is renewed each year on this day. God grants a person on Shabuot the ability to think of new Torah insights, and one must therefore pray on Shabuot for Torah knowledge and the wisdom to understand to the best of his soul's capability, and also try to think of "Hiddushim" during his study on Shabuot.
During the day of Shabuot, too, one should try to minimize his sleeping in order to spend as much time as possible involved in Torah learning. Every moment spent learning on Shabuot earns a person reward, and one must not squander this opportunity. In fact, there were great Rabbis who would not sleep at all on Shabuot; after remaining awake throughout the night, they would simply continue learning through the day of Shabuot. The Hid"a (Rav Haim Yosef David Azulai, 1724-1806) likewise advises against indulging in sleep on the day of Shabuot. He also emphasizes that one must ensure not to fall asleep during the prayer service.
Finally, one should also devote himself to Torah study with extra vigor and diligence during the "Sheloshet Yemeh Hagbala" the three days of preparation prior to Shabuot. Just as in the wilderness Beneh Yisrael were instructed to abstain from relations and prepare themselves for three days prior to Matan Torah, so must we increase our efforts to learn Torah and minimize our physical indulgence during these three days. Hacham Ben Sion writes that the level of inspiration one receives from the experience of Shabuot depends on the amount of effort he exerted during the three previous days to prepare for this great experience.