Around the end of the afternoon beginning of the evening of the Rosh HaShana (around 18:30)
A Noahide should Start his Prayer with Psalm 24.
Keep in mind that the focused recitation of Psalm 24 is the vessel for all of a person’s needs through the entire year as it was revealed by the Rebbe Rashab.
You should have the following in your mind: while reciting:
The first verse: That the entire earth belongs to HaShem et only His Blessing allows men to make a living on it. His physical work is not the cause of his earnings but the vessel to receive the Divine Blessings. (From Sefer HaMaamarim 5666, page 335).
The third verse: The service of HaShem is compared to the ascension of a mountain. In this situation, in order to avoid the fall, one needs constantly to be in a movement of ascension, so to in the Service of HaShem. (Likutei Sichot 18, page 127)
Fourth verse: “Clean hands” is the one who runs from evil and a “pure heart” is the one who has no other desire then the Service of HaShem. It is such a person who may “ascend towards the mountain of HaShem” (From Sefer HaMaamarim 5666, page 394). The mountain of HaShem is referring to the Garden of Eden, which is the reward for those faithful Noahides who studied Torah in a propre way with proper Jewish Guidance “those with clean hands”. The resurrection of the dead is for those Bnei Noah (together with the Jews) who accepted the Seven Commandments and fulfilled them because HaShem commanded them in the Torah to Moses and the Jewish Nation to teach the Nations, and therefor they need to apply them according to Jewish Guidance, those are “the one’s with a pure heart”. Furthermore, the means to accomplish our purpose is by revealing G-dlines in the physical world through the fulfilment of the Seven Commandments (which includes proper Torah Study).
Seventh Verse: When King Solomon wanted to bring the Holy Ark into the Holy of Holies in the Temple, the doors remained close until he invoke the merit of his father David. Only then the doors open up (Rachi). We are talking here about two set of “doors”. The “ lower doors” on one hand which refer to the transition between intellect and the emotions, which gives rise to the “higher doors” on the other hand which is the emotional direction which is manifest in the midst of pure intellect( Sefer Ha Maamarim 5672, page 263)
If the fulfillment of one's prayer would result in the sanctification of God's Name, he should pray that God act for the sake of the holiness of His Name. One should also invoke the merit of his ancestors, for we know that "the righteous are greater in death than in life"
Of David, a song. The land and the fullness thereof are the Lord's; the world and those who dwell therein. 2. For He founded it upon seas and established it upon rivers. 3. Who will ascend upon the Lord's mount and who will stand in His Holy place? 4. He who has clean hands and a pure heart, who has not taken My name in vain and has not sworn deceitfully. 5. He shall receive a blessing from the Lord and charity from the God of his salvation. 6. This is the generation of those who seek Him, who seek Your presence-Jacob, forever. 7. [You] gates, lift your heads and be uplifted, [you] everlasting portals, so that the King of Glory may enter. 8. Who is this King of Glory? The Lord, Who is strong and mighty, the Lord Who is a mighty warrior. 9.[You] gates, lift your heads and lift up, [you] everlasting portals, so that the King of Glory may enter. 10. Who is this King of Glory? The Lord of Hosts-He is the King of Glory forever.