I may regret this, but if you really do want to know.....
Yes, for the most part it is very similar to a hands on prayer. The rules differ from tradition to tradition though. Most agree that you can't mess around with free will, and you will get back what you send out. This means that you have to think carefully about any spells you may want to cast.
Like for instance, say I wanted to cast a money spell. This also varies, but I was taught that there is nothing wrong with asking the universe for what you need to get by. After all, in order to take care of others you must first take care of yourself. I can't help the homeless if I'm one of them. However, if I were to cast a spell to win the lottery, that's greed. The backlash would not be pretty. A book we have warns about this because I could ask for a million dollars, and wake up to find it on my porch, only to learn later that it was from a bank robbery and the real robber ditched it to avoid getting caught, and now it's pinned on me.
That's a bit of an extreme example, but it gets the point across. Another thing you often find is that most teachers will tell you not to get into actual casting until you've studied for a year. Mine didn't, but I understand the reason for this. People who don't know what they're doing can get themselves in trouble. I got a big surprise when I started.
Something else to keep in mind is that it's not generally a good idea to always go rushing into a magical solution. Spells are a tool, but not the only one available. If there is something non magical you can do to achieve the same result, it's usually better to go with that option. If you go running to your spell book for every little problem you become dependent, and that's not a good thing.
As for what magic is, as I understand it, it is using your energy to bring about your goal. The forces of the universe are made up of energy, as are we. That's why most teachers and books will tell you to create a sacred space where you won't be interrupted. The ability to concentrate and visualize is very important. I guess you could look at it as a mind over matter type thing. Me, I like to keep things simple. My altar is my coffee table, and my 'cauldron' is a cake pan. As far as I'm concerned intent is all that matters. Others will insist you need a circle, a special altar, proper tools, ect... There really is no wrong way because spell casting is such a personal thing. If you're not comfortable then it isn't likely to work.
That's also why it's recommended that you write your own spells. That way your energy goes into the creation and it's more likely to work if you did it right. It also lets you tailor it to your unique situation. There's a system to it; stating the problem, then the change you want to take place. I either write my own, or change around someone else's. I don't mess with it often either. Like I said, it requires careful consideration.