Not the magical if-we-massage-God's-ego-and-ask-nicely-enough-he'll-grant-wishes power -I think that's juvenile hogwash- but the real power that comes from following the instructions.
In the cultural tradition of Protestant Christianity that I grew up in and am most familiar with, Jesus says some important things about what prayer is for who it's meant to benefit, and how you're supposed to do it:
And when you pray, do not be like the hypocrites. For they love to stand and pray in the synagogues and at the street corners, that they may be seen by others. Truly, I say to you, they have received their reward. But when you pray, go into your room and shut the door and pray to your Father who is in secret. And your Father who sees in secret will reward you.
“And when you pray, do not heap up empty phrases as the Gentiles do, for they think that they will be heard for their many words. Do not be like them, for your Father knows what you need before you ask him.
Pray then like this:“Our Father in heaven,
hallowed be your name.
Thy kingdom come,
thy will be done,
on earth as it is in heaven.
Give us this day our daily bread,
and forgive us our trespasses,
as we forgive those who trespass against us.
And lead us not into temptation,
but deliver us from evil.
I love this passage. (It's Matthew 6:5-13)
There are lots of different versions, I just wrote this one out as I remember it, but I got the gist. And I think it's a pretty good gist.
If you break it down, you have a step by step workout to build an ethically primed and caring mind. It's a pre-formed mold to pour your thoughts through and when they come out the other side you're ready to be a better person than when you started.
[NOTE: I'mma break it down from a perspective that disregards god as a being with a consciousness and personality, and instead treat 'god' as a placeholder for the immensity and awe of the universe 'cause that's how I roll. Your mileage may vary.]
Check it out:
The preamble: Here's where we're told what prayer is for, and who it benefits. It's not about showing how pious you are, and making a big show of praying undermines the true benefit. So to avoid that, we're told to go into our room pray in secret, because the only people who need to hear you pray are you and God. And truth be told, God doesn't need to hear you ask for anything -God already knows what's up. So when you pray, you're the person who needs to listen.
Also, it doesn't take much, so don't overdo it.
Pray then like this: Here we go, short and sweet.
Our Father in heaven, hallowed be your name: Begin by recognizing how awesome the universe is. It's massive beyond imagining, beautiful, terrifying, and sacred.
Thy kingdom come, thy will be done: Recognize that you do not get to decide what the universe does. It is bigger than you can imagine, moving in ways you cannot perceive or understand, according to laws that we have to build absurd mental and mathematical structures to allow our consciousness even an approximate understanding of the most basic things about it. Like, whoa.
on earth as it is in heaven: Recognize that even though there are awesome things like Gamma ray bursts and black holes and other objects, forces, and events that are so immense we have difficulty even imagining their scale, you are a part of this universe, and exist in concert with all other things, no matter what or where they are. You are not an outside observer, but an inexorable part of its magnificent machinery. This means the things you are and do matter, even though you may not have the final say in how.
Give us this day our daily bread: It's ok to hope things work out for yourself and others. It is never wholly up to you, but as we just discovered, even in the vast ocean of the cosmos, what we do in our little drop has meaning.
and forgive us our trespasses, as we forgive those who trespass against us: Call them what you like, debts, sins, trespasses, there is no living as a person without doing harm or depending on others. You need to accept that you are not perfect, and will always owe someone, somewhere an apology or a thank you. Often both, and you're unlikely to get around to settling accounts, so be ready to accept and love other people who need your help, or do harm. And now that you recognize what you owe, you can focus on doing right. Apologizing for your trespasses, atoning for your sins, and paying your debts -back or forward.
And lead us not into temptation, but deliver us from evil: Now that we're almost done praying, it's important to recognize that we're NOT done. 'Lead us not into temptation, but deliver us from evil' shows us that we're setting out on a journey, not finishing up a chore. Temptation and Evil are where we don't want to go. By ending this way, we remind ourselves how easy it is to be selfish or self-righteous when we want to.
Just because we're done praying doesn't mean we should stop thinking and caring the way we did while we were praying. We should hold on to that momentum and go out of our rooms and into the world centered and ready to do good.
My experiences with Zen mediation in Japan and Seon meditation in Korea have always included a 'walking meditation' after the sitting one. And I think this is because meditation/prayer is the warm-up before you go on the the main event of being a good person in the world.
This is why I object to people, particularly conservative politicians, prattling on about 'Thoughts and Prayers' for the victims of hardship. They are the 'hypocrites' Jesus warns us not to be. All their public protestations of piety do is stake a claim to an ideological 'high ground' to build their mansions on and fences around and never come out of to do any of the real work Jesus is constantly asking people to do.
If you want to think and pray, by all means please do. And yeah, even though prayer is primarily for your benefit, I think directing your thoughts toward someone you want to help or something you want to accomplish is good. After praying, you're primed to notice things you can do and act with perspective and caring, and directing that focus at people or projects is worthwhile.
But if praying is all you intend to do, then you're doing it wrong.