Personally I look at the idea of prayer as a combination of meditation and magic. It is meditation, in that a person uses prayer as a method of personal reflection. People sit and find a sense of stillness, then turn their thoughts towards a specific statement or chant while contemplating an idea or problem.
Prayer is also like magic in that it is a focused plea towards an external force to receive assistance in some form- be it for protection, absolution, guidance, or inspiration. It is a process of focus, contemplation, committing honor or recognition of an outside helping force, and asking that force to assist you in reaching particular goal.
The process of prayer is actually fairly simple. First consider what you want to pray for. And through that understanding, choose or write an appropriate prayer to say. In that prayer itself there is a formula of recognizing the being you are praying to, recognizing their spheres of influence, being thankful for their presence and influence within your life, and then asking for assistance.
The Lord's prayer is actually a very good example of this formula, and can be used as a solid basis for the process in other prayers as well. Which is why in the bible it begins by stating "Pray then like this" as to say that this is not merely -a- prayer, but instruction on -how- to pray.
"Our Father in heaven, hallowed be your name."; recognizing the presence of god
"Your kingdom come, your will be done, on earth as it is in heaven."; your will defines our reality- recognizing god as the creator force and dominant over everything.
"Give us this day our daily bread, and forgive us our trespass, as we forgive those who trespass against us. And lead us not into temptation, but deliver us from evil."; This is the actual request or purpose of the prayer. In this case, asking for continued protection and guidance in life, spirit, and morality against their respective sources of negative influence. IE; "Help me be the best person I can be."
there are so many ways to pray really. you can even say the words in your head. but for me, personally, I like to do it outside a lot. I have a special connection to nature, so I tend to feel best praying in a natural setting. however, I will still also do it wherever else. I pray when I get up in the morning, in noon, before rituals, before eating, and when going to bed. and whenever I'm thankful for something or need help or protection or whatever like that.