How do I ask G-d to fulfill my needs?
Question: Perhaps I should pray to G-d more often or more fervently? And how do I nurture a habit within myself to ask G-d to fulfill my needs?
Answer: It is certainly meritorious to pray to G-d for one’s own needs, as well as for the needs of others, and for the general needs that all people have. It is also meritorious to combine these requests with thanks and praises to G-d.
Rabbi J. Immanuel Schochet, o.b.m., provided a Noahide “Amidah” ["standing"] prayer, which is appropriate for Noahides to say on a daily basis if they wish, with any appropriate changes they wish to make:
A Noahide “Amidah” Prayer
(Copyright ’09 by Ask Noah International)
Blessed are You, G-d, the Supreme Being who bestows abundant kindness.
Please endow us graciously with wisdom, understanding and knowledge.
Please accept our repentance, and forgive us for our errors and sins.
Grant complete healing for all our wounds and ailments.
Bestow upon us all the needs for our sustenance from Your bounty.
Hasten the day of which it is said, “G-d will be King over the entire earth; in that day G-d shall be One and His Name One” ; “For then I will turn the peoples to pure language, so that all will call upon the Name of G-d to serve Him with one purpose,”  and “They will not harm or destroy on all My holy mountain, for the earth will be filled with knowledge of G-d as water covering the sea bed.” 
Hear our voice, G-d, our merciful Father, have compassion upon us and accept our prayers in mercy and favor. Blessed are You, G-d, who hears prayer.
 Zechariah 14:9
 Zephaniah 3:9
 Isaiah 11:9
For more on this subject, please see this page of our Q&A Forum:
Praying for Needs