The concept of "prayer" in Buddhism can be a delicate one, ripe for controversy, although it doesn't need to be. Some Buddhists interpret Buddhism as an essentially rationalist philosophy, compatible with science, and see 'prayer' as possibly unnecessary at best or, at worst, misleading. Others actively and regularly pray to the Buddhas and bodhisattvas, and do ask for both spiritual and material benefits. Which is correct?
Before we can answer this question, we should ask ourselves, what does prayer do? What does prayer do for me, and also, what does prayer do for others? Is "prayer" the same for all religions, or do different religions approach it differently?
Prayer, as practiced in the United States, is of course imbued with Christian tradition, so it is difficult to even think of the word, "prayer", without assuming that it involves addressing a speech to a deity (God), and asking for some thing, either spiritual (peace of mind, happiness) or material (health and wealth), for oneself alone, or for others (bless my family, friends, nation, etc). Prayer does not always include the act of requesting; it can be considered as an act of submission or devotion to a deity. Prayer can be very versatile. As a Navy Chaplain, prayer is an essential part of my job: prayers are involved in retirement ceremonies, change of command ceremonies, Evening Prayer (Tattoo) over the 1MC at sea, and so forth. Who can do prayers, and what language is used, can cause enormous controversies! People in America take prayer VERY seriously.
Prayer, in the Buddhist traditions, does exist. We may call it by other names (blessings, mantras) but the essence is similar. Prayer in Buddhism may have begun as a form of "recollection" of the Buddha following his parinirvana; it was a way to "recall to mind" the Buddha and his teachings. Most traditional prayers I have encountered are addressed to the Buddha or to the Bodhisattavas, the Bodhisattva Kannon (Kwan Yin), who manifests Compassion, being a most popular example. Prayers both serve as a way to praise the virtues of the Buddha, and to give us a focus for the directing of merits, to oneself or others. Not all traditional forms of Buddhism emphasize prayer, such as Jodo Shinshu, which discourages it because of the doctrine of Self-Power (jiriki) yet even nembutsu recitation is a verbal method for us to focus on the merits of Amida Buddha and our own potentiality for Buddhahood. In this way, prayer serves the same purpose as having a statue or image of Buddha: we are not "worshipping" the physical images, the same way we are not using "prayer" as a substitute for practice. Prayer is an upaya or "skillful means" towards fully understanding the holistic nature of the Three Treasures: Buddha, Dharma, Sangha. We can call this being respectful of the Buddha, mindful of his Teachings, and actively participating within the human community of Buddhists.
That is why I think it would be improper to declare what is a "right" form of Buddhist prayer, since there are so many different traditions and practices, just as there are different ways to chant or recite the sutras. Are there Buddhists who believe in prayer for material benefits and protection? There are! There are also Buddhists who do not rely on prayer, who may focus primarily on study and meditatiton. Buddhist prayer simply is one Buddhist practice among many, which some may accept and others reject.
For Buddhist Lay Leaders in the military, it is difficult to avoid the concept of prayer, so if you have not practiced this before, don't get hung up on the word itself, and try to understand it as upaya: would there be people who may benefit from hearing a blessing of Buddhist teachings in English? I would recommend that prayers be short and to the point (no one likes a long Evening Tattoo!), inclusive, while remembering that we are not trying to do Christian prayers disguised as Buddhist ones (for example, I do not have a problem with using "Lord" or "World-Honored One" in place of Buddha, but it would be a stretch to use the word "All-Mighty")! We don't have to "ask" or request a favor or privilege, but we can use words that recall us to mindfullness of concepts like peace, honor, courage, vigilance, etc. Certain sutras like the Metta (Loving-Kindness) Sutta can be adapted to a prayer-format.
Buddhist prayer may not be practiceable by everyone, due to its very personal, and emotional nature. You have to be comfortable with the idea of this particular use of language. As in other religions, no one respects an insincere prayer! Practice writing down or verbalizing what you would say, and would want to hear.
Namo Amida Butsu