As mentioned, in the time of the Rishonim, most Jews fasted on Erev Rosh Ha-shana (SA 581:2; MB ad loc.16), while today most do not. A few people still fast half the day or until plag ha-minḥa. Others give charity in place of fasting.
Ashkenazic custom is to recite many more Seliḥot on Erev Rosh Ha-shana than on other days. If Seliḥot begin before dawn, Taḥanun is recited at the end of the Seliḥot service. Even then, Taḥanun is not said following Shaḥarit, as Taḥanun is normally not recited on Erev Yom Tov. If Seliḥot begin after dawn, Taḥanun is not recited at the end of Seliḥot either (MB 581:23).
On Erev Rosh Ha-shana we do not blow the shofar, so as to distinguish the custom-based blasts of the month of Elul from the obligatory blasts of Rosh Ha-shana (SA 581:3; Levush). Some are stringent and do not even practice blowing the shofar on Erev Rosh Ha-shana. However, one who wants to practice may do so in a closed room (MA ad loc. 14; Eliya Rabba ad loc. 4; MB ad loc. 24).
Since Rosh Ha-shana is called a sacred occasion (mikra kodesh), we honor it as we do Shabbat and holidays. We prepare for it by cleaning the home, doing the laundry, showering, preparing festive meals, and setting the table nicely. If one needs a haircut or a shave, it is a mitzva to take care of it beforehand, in honor of the holiday (SA 581:1; below, 3:4).
As a good omen, in hopes that the upcoming year will be filled with abundance, it is customary to make particularly good and plentiful food for Rosh Ha-shana. To enable this, common practice was to slaughter many animals before Rosh Ha-shana, for the festive meals. In fact, Erev Rosh Ha-shana is listed in the Mishna as one of the four days of the year on which the most animals were slaughtered. Therefore, special care had to be taken to avoid slaughtering an animal and its offspring on the same day, which is forbidden (Ḥullin 83a).
Some have the custom of going to mikveh on Erev Rosh Ha-shana, to purify themselves in anticipation of the Day of Judgment (Rema 581:4). One who wishes to follow this custom but finds it difficult may wash with nine kavim (approximately 11 liters) of water instead (MB ad loc. 26). That is, he should stand in the shower while nine kavim of water streams down on him without interruption. He should ensure that this water comes into contact with his entire body (Peninei Halakha: Festivals 1:16 and n. 8).
It is customary to do hatarat nedarim (nullification of vows) on Erev Rosh Ha-shana. During the recitation, future vows are disclaimed as well (as we will explain below, 5:11-12).