"An act of spiritual communion" is the best definition that I have found for prayer. It's a term that makes a lot of the Pagans that I've met uncomfortable. I think that it's likely that that comes from association with ritual rendered meaningless through repetition or lack of comprehension as well as its association with supplication; not all prayers are a request for Divine aid, however.
By the above definition, nearly every spiritual behavior could be considered an act of prayer. Most religions have proscribed techniques for this. Repetition of phrases and holy texts, meditation (often in the form of silent repetition of the same), self denial in the form of fasting or a form of abstinence, and sacrifice or offering seem to be the most common techniques. Less common in modern forms of religion are physical exertions such as dancing and martial arts, ritual intoxication, self-mortification and mutilation, and application of physical pain and pleasure.
I personally feel nearly any of the above-named techniques can be valuable in establishing or strengthening a connection with the Divine. Nearly any activity, given the proper framework, is a prayer. Many feel that their paths do not allow them the flexibility to explore other forms of worship, and though I am not one who appreciates restrictions on expression in faith, I believe that their may be a valid reason for these beliefs.
An act of communion is one of interaction. A connection to the essence of the aspect of the Divine that one is attempting to interact with seems to be facilitated by several factors. Achieving a resonance with the essence of that Deity is, appropriately, essential. Many of the props that are used in prayer are related to the mythology of the deity involved in the act, which helps to both establish a proper frame of mind for the participant and to, through sympathetic resonance, attract the attention of that which it is like. Personal will or passion also seems to be important; often the most remarkable petitions are the ones granted in times of need for the petitioner, and the petitioners do not always have the opportunity to be in an established sacred space, surrounded by the trappings of their faith.
An act that is alien to the paradigm of a faith is less likely to achieve the appropriate resonance and less likely to establish the proper frame of mind within the person preforming the prayer. Considering the variety of individual human expression, however, it is inevitable that there will among any group arise segments who perceive through their own gnosis connections not made with that aspect of the Divine by the more orthodox members of that group. Gnostic Christians and Sufi Muslims are good modern examples of such subgroups.
There have been many studies and articles about the benefits of prayer. I tend to think the benefits of most prayers include the benefits of the associated activity (mental or physical exercise, purging of one's system through fasting, mental purging and resetting through meditation) as well as an increased connection to the aspect of the Divine that one is praying to. The second benefit is the most ephemeral in the immediate (although the emotional pleasure and raising of one's spirit by improving such a connection should not be overlooked) but most important in the long term. Drawing close to that which you worship allows it a closer connection to you as well thus allowing it a greater influence over your life. I believe that the Gods can affect us despite spiritual distance, but I also believe that their aid can be more direct when given a channel through which to pour their energy and will.
I raised the subject of the repetition of prayer earlier. Regular acts of prayer give one a chance to remember why we revere the Gods that we do, and give those Gods an opening with which to reach in and affect our lives. Just as daily exercise, learning and meditation are beneficial to one's physical and mental well-being, prayer improves the tone of one's energy and spirit.
At the same time, I've noticed that it is helpful to alter one's prayers occasionally. Repeating something endlessly can cause it to lose its meaning; this can be observed personally when one repeats a word to the point when it sounds strange in their ears. If one feels that certain acts of worship have grown stale, substituting them for another can help them in getting out of such a spiritual rut. It is important to keep in mind the personal signifigance of words and gestures when doing this. If an invocation or mantra feels like it has been overused, substitute words of the invocation for fresh ones with greater or equal spiritual signifigance to you. Not everyone is a poet or author but most dieties have a body of liturgy associated with them from which new names, attributes and adorations can be drawn. Barring that a good thesauraus can be of great help.
In the case of non-verbal prayers or prayers for which words are only a part, similar substitutions can be made. Change a gesture in a dance, abstain from a different substance or act than the usual, or seek a new offering that might add new signifigance to your relationship with your chosen deity.
Prayer is any act of devotion or attempt to commune with the Divine. This can include invocation, spoken words and phrases, meditation, dance, purification or cleansing, eating and drinking, walking, or working on a project related to the Divinity you are attempting to improve your connection with.
Prayer may be done at any time of day or night.
Actions, props and words associated with the aspect of the Divine in question increase the potency of a prayer, as does an established space sacred to said deity.
Prayer is beneficial because it draws you closer to the Divine and your chosen Gods and gives them a channel by which they may affect your life more directly.
If a prayer feels meaningless or stale, alter parts of it, or substitute it for a different act of worship. This will allow your relationship with your Gods to grow in other directions, and helps to keep it fresh and interesting, which is important for beings with linear minds like our own.
Embrace your Gods. Let them embrace you. Grow close to the Divine. Pray!
"Let my worship be within the heart that rejoices, for behold, all acts of love and pleasure are my rituals. Therefore, let there be beauty and strength, power and compassion, honor and humility, mirth and reverence within you.." - The Charge of the Goddess