The Gemara (Rosh Hashanah 16:) states that three sefarim are opened in heaven on Rosh Hashanah. One sefer is of perfect tzaddikim, one is of resha'im, and one of beinanim (people between tzaddikim and resha'im), and each person is inscribed in one of these sefarim. If he is written in the sefer of tzaddikim, he is immediately destined to have a good year with peace and blessings.
We are used to thinking that to be written in the sefer of tzaddikim, one had to have lived the previous year like a tzaddik, or at least, have done teshuvah and is therefore worthy to be called a tzaddik.
However, Toldos Yaakov Yosef (Re'eh) expresses it innovatively. He writes that it is dependent on how one plans to live the upcoming year. If he plans to live the year as a tzaddik (to be cautious with the mitzvos, etc.), he will be inscribed in the sefer of tzaddikim and immediately written for a good year of life and peace. If a person plans to live like a beinoni or a rasha, he is inscribed in those books and will be judged accordingly.
One of the primary themes of Rosh Hashanah is announcing that Hashem is king and requesting that Hashem's kingdom be known to every creation in the world.
Many of the tefillos of Rosh Hashanah are based on this theme. The mitzvah of shofar is also about proclaiming Hashem’s kingship. Reb Saadyah Gaon explains that it is customary to blow shofar when crowning a king. Therefore, we have a mitzvah to blow shofar on Rosh Hashanah, because we crown Hashem as king on Rosh Hashanah.
The Gemara (Rosh Hashanah 16.) says לפני אמרו עליכם שתמלכוני כדי מלכיות, Hashem says, "Say Malchiyos (in Musaf) before Me so I will be made King upon you."
The Ma'or v'Shemesh explains that this means you should "say the Malchiyos on Rosh Hashanah wholeheartedly because then you will be able to make Hashem King the entire year."
The segulah of saying Malchiyos and thinking about the reality that Hashem is King will help you recognize that throughout the year.
It is known from the Lechovitzer zt'l that speaking about emunah brings us emunah. He said (Tehillim 116:10) אדבר כי האמנתי, I believe in Hashem because I talk about emunah. This is also alluded to in the words לפני אמרו מלכיות, speak about Hashem's kingship. Repeat the pasukim of Malchiyos and say other tefillos on Rosh Hashanah about Hashem's kingship. Speaking about it will bring you the emunah.
Therefore, words and thoughts of emunah should constantly be on our minds during Rosh Hashanah. Think thoughts of emunah, such as, "Hashem sees everything. He leads us with hashgachah pratis. Everything that occurs is from Him..." Think these and similar thoughts, say the tefillos that discuss Hashem's Kingship until we will feel in our bones the message that "Hashem is King." This emunah will draw onto us emunah and deveikus for the entire year.
Furthermore, the emunah will be our merit to be granted a good year.
Yaaras Dvash (vol.2 drush 1) writes that the ten days of Aseres Yemei teshuvah correspond to the Aseres HaDibros. The first two days correspond to the first two of the Aseres HaDibros, אלהים לך יהיה ולא ...אלקיך 'ה אנכי אחרים, the two mitzvos that discuss having emunah in Hashem. Therefore, the ideal time to focus on emunah is the first two days of Rosh Hashanah.
Shem MiShmuel (Nitzavim 5673) writes, "An important lesson for a G-d fearing Yid is that during the yomim noraim, he shouldn't be cold. Instead, he should perform all of the mitzvos of this seventh month with a lot of hislahavus and emotion. If he does so, he will succeed in the judgment. Each Yid will receive a good judgment in accordance with his hislahavus." Living with emunah in Hashem and knowing that Hashem hears us, watches us, and cherishes our mitzvos and good deeds will help us serve Hashem in this month with immense hislahavus. We begin attaining this emunah on the first two days of Rosh Hashanah. This is when we say Malchiyos and make Hashem our king and the King of all creations. We will know that Hashem is our King on Rosh Hashanah, and the entire year.
Additional Insights
1. The Trisker Magid (Magen Avraham, beginning of Vayikra) writes that when Esther became queen, the king sent gifts to his subjects (see Esther 2:18, עשה למדינות והנחה). This is the custom of kings and queens; when they are coronated, they give gifts to their citizens. So, on Rosh Hashanah, when, keviyachol, we have the privilege to crown Hashem as King over the world, Hashem bestows His many brachos on us. The Gemara (Rosh Hashanah 11.) states that the slavery in Mitzrayim ended on Rosh Hashanah. Similarly, each person can leave his problems on Rosh Hashanah.
2. The Rebbe of Dzurik, zt'l, said that the difference between a מלך and an אדון is that an אדון is a king who rules as he desires, without taking advice from others. A מלך asks for advice from others. (One of the translations of מלך is to seek counsel from others. See Brachos 27: בדביתהו ואמליך אזל, "He went and conferred with his wife.") The Rebbe of Dzurik said that during the holocaust, Hashem acted as an אדון because He didn't accept the tzaddikim’s counsel. The Machnovka Rebbe zt'l (who was a son-in-law of the Rebbe of Dzurik) added that on Rosh Hashanah, when we say Malchiyos, and crown Hashem as king, one of the gains is that now Hashem will lead us like a מלך and not as an אדון, and He will take counsel from the tzaddikim.
3. Ma'or v'Shemesh writes, "Hashem created the entire world so that every creature should be aware of His kingship, that He rules over everything... Hashem chose us as His nation, to keep His mitzvos, and to declare His oneness twice a day (during Shema)... Throughout the year, most people can’t accept Hashem's kingship with perfection... [Due to aveiros and the yetzer hara’s pull, it is hard for people to internalize the truth that everything is from Hashem.] However, on Rosh Hashanah, we should make Hashem our king with love and all our hearts. This will strengthen us to make Hashem 'one' when we say Shema the entire year... Fortunate is the person who merits to have holy pure thoughts of uniting Hashem... during the forty-eight hours of Rosh Hashanah, because this will infuse him with kedushah and deveikus for the entire year. Each moment of Rosh Hashanah gives strength... to internalize the entire year that Hashem is King." Similarly, Pele Yoetz (Rosh Hashanah) writes, "If only a person's heart would be filled with yiras Shamayim on Rosh Hashanah... This would grant him chiyus for his soul for the entire year."
4. It states (Tehillim 17:2) יצא משפטי מלפניך. This means that Hashem will judge us favorably, on condition that מישרים תחזינה עיניך, we should look at everything through eyes of emunah. It states (Tehillim 33:22) לך יחלנו כאשר עלינו 'ה חסדך יהי. Reb Moshe Leib Sassover zt'l explains: We ask Hashem to bestow His kindness upon us, even though He sees that we are unworthy. The reason is לך יחלנו כאשר; we trust in Hashem although we never saw Him, so, too, Hashem should bestow His kindness on us, even when He doesn't see us as being worthy of His kindness.
5. Tosfos (Rosh Hashanah 33:) says that the one hundred shofar blasts we blow on Rosh Hashanah correspond to the one hundred sobs Sisera's mother cried when her son fell in battle. Chazal say that a malach counted her tears, and she cried precisely one hundred times. We wonder about the connection between the mitzvah of shofar and a non-Jewish woman’s tears over her wicked son’s death. But we can explain that this is the lesson we want to learn on Rosh Hashanah. Everything is from Hashem, and even the number of a non-Jewish woman cries is also counted and is with hashgachah pratis. Nothing happens by chance.
6. Shem MiShmuel explains that even the very best of the goyim (העולם אומות חסידי), don't perform their good deeds with hislahavus. When a Yid serves Hashem with hislahavus, this demonstrates that we are far superior to even the best goy, and this helps us receive a favorable judgment on these days.
7. Many readers remember that on the 12th of Kislev פ"תש, a shooting took place at a Jersey City grocery store, r'l. May Hashem protect us from all tzaros. One yungerman, a melamed, was coming home from cheder when the shooting began. He was worried that his wife was in the grocery as she had told him she would be there at about that time. Fortunately, he found his wife alive and well at home. She told him she had planned to go to the grocery, but when she opened the door, she saw a package at the doorstep. It was some clothing she ordered right after Yom Kippur for the sake of tznius. (On Yom Kippur, when the chazan was singing Unesaneh Tokef, she made a kabbalah to wear a particular type of tznius garment. she ordered it, but it took some time to arrive. It had arrived that day, just as she prepared to leave for the grocery. She decided to put it on before going to the grocery, and that is when the shooting began. She was saved thanks to her kabbalah.