Tachnun (confession of sins) and similar prayers are omitted.
It is customary to begin working on -- or at least planning -- the construction of the sukkah immediately after Yom Kippur. Indeed, The Midrash (Vayikra Rabbah 30:7) describes the four days between Yom Kippur and Sukkot as a time when the Jewish people are "preoccupied with mitzvot... this one is occupied with his sukkah, this one is occupied with his lulav..."
According to an old Chassidic tradition -- mentioned in the writings of the Baal Shem Tov -- the day after Yom Kippur is referred to as "G-d's Name." (The Baal Shem Tov explains that each of the various divine names describe G-d's involvement in a specific "world" or realm of reality, but the designation "G-d's Name" -- without reference to any particular name -- connotes a divine effluence that transcends all realms and particulars. On Yom Kippur, we access and reveal the very essence of our soul, which is one with the very essence of G-d; thus the day after Yom Kippur carries the designation "G-d's Name.")