Erev Rosh Hashanah
Saying Tehillim on Erev Rosh Hashanah:
The Tzemach Tzedek of Lubavitch zy"a (quoted in Sefer Sichos Hashana, 5705, Erev Rosh Hashanah, Ois 4) states that on erev Rosh Hashanah, one should spend time reciting Tehillim from the depths of his heart. However, he adds that the recitation must be with great joy "because when soldiers go out to war, cities cannot be conquered with tears; rather, they always march with a happy tune."
Teshuva With Joy:
The Magid of Kozhnitz zy"a (Sefer Avodas Yisroel, Parshas Netzavim) writes that teshuva must be done with joy and with bitachon that Hashem will never abandon His nation. He says that the reason we do not recite Tachanun on erev Yom Kippur may be to show that we are not falling on our faces with sadness; rather, we stand up and express our joy and love for Hashem.
Rectifying the Entire Year:
The Gemara states (Rosh Hashanah 2B) that when it comes to a king, one day is considered like an entire year. Sefer Chesed L'Avrohom (on Rosh Hashanah) writes that the same idea applies to someone who comes to the King of Kings to do teshuva. Even if someone did not properly serve Him all year, and only returns to Him at the very end of the year, it is considered as if He acted correctly for the entire year. From this, we can see how kind and merciful Hashem is. Even if one only returns to Him on the very last day of the year, He allows him to use this day to rectify the entire year.
Uplifting the Entire Year:
My grandfather, the Admor of Kretchnif zy"a, would say that this is the reason we still recite the words "bareich aleinu Hashem Elokeinu es hashana hazos (bless this year)" during Minchah of erev Rosh Hashanah, even though the year is almost over. We see that even the final moments of the year can still be considered a full year of goodness!
Sharpening Knives on Erev Rosh Hashanah:
It is written in the writings of Rav Chacham Tzvi Halberstam zt'l (quoted in Sefer Hachaim) that erev Rosh Hashanah fell out one year on a Monday, and a large crowd arrived in Sanz before Shabbos to spend the holy day in the presence of the Divrei Chaim zy"a. That leil Shabbos, while Rav Chaim was conducting his tish, he began to cut the challos and realized the knife was dull. He expressed his disapproval to the gabbaim who had failed to sharpen the knives. One of the guests overheard what he said and decided that he would sharpen the knives, and he did so right after Shabbos. On leil Rosh Hashanah, when Rav Chaim saw the knives, he loudly asked, "Who sharpened these knives?" The guest was afraid to open his mouth. He was scared that Rav Chaim would be upset at him for sharpening the knives without permission. However, Rav Chaim then called out, "Whoever sharpened the knives should be blessed to live until 120!" When the guest heard this, he said out loud, "Rebbi, I want all 120 years, not a day less." Rav Chaim nodded his head. And so it was! The man lived a full 120 years. On the last day of his life, he got into a fight with a huge gentile in the city's street. When he was asked why he wasn't afraid of the non-Jew, he answered, "I'm not afraid of anything. I know that I still have one more day to live." And so it was. Rav Y. Horowitz of Dzikov zt'l knew this Jew and testified to his age.