There are many different explanations as to "how it works". These range from greater connections with supernatural beings to just giving your brain some quiet time to perform various housekeeping activities that it doesn't get a chance to do when constantly stimulated with computer/phone/tv.
If you want to know "what can meditation do for me besides waste my time?", here is my attempt at describing what it feels like and how it's beneficial. This is just my subjective experience.
The first benefit of meditation for me has been to make me aware of the near-constant mental chatter going on in my mind, and presumably the minds of many other people in society. I knew it was bad but I had no idea how bad until I tried to shut it off for a few minutes. It's like when someone points out every time you say "umm" in a conversation and you suddenly become aware you are doing it constantly.
As for the second benefit, imagine how you feel when you are in a pleasurable and carefree mental state. For example you are at a bar or a party talking to someone you just met who has similar interests and after 20min you have sort of a full body buzz going even if you haven't been drinking, the rest of the world falls away, and time flies by. Or if you go to the gym or do martial arts and you enter the gym stressed about work, then two hours later you walk out and are driving home, feeling great and the things that were bothering you earlier seem insignificant. Meditation builds a mental muscle that allows you to more easily slip into that groove. I'm still a newbie but there are times that I can slip into that state at will, walking down a crowded street surrounded by people.
"Arrgg! stop wasting my time and tell me how this is this going to get me money/sex/stock options!"
If you are still looking for the immediately tangible benefit of meditation in terms of (input x) -> (output y) that will depend on your situation. I can however give you an example. If there is a room full of of stressed out uptight people and someone walks in who is more relaxed and "present" than everyone else in the room, other people in the room will notice this, they will subconsciously assume there is a reason, they will be more inclined to listen to that person. They are walking around with empty cups and that person acts like their cup is overflowing.
The joke is the first time this happens you will have the thought "omg it's working, the 'trick' is working!" and instantly your new found charisma will evaporate. If you chase it you cannot have it, there are many things in life like this :]
As for method, I don't use candles, music, darkness, unusual sitting poses, or any other props. They obviously help some people but I have not tried them. I simply put my phone on silent, set my phone alarm to vibrate in 20min and put it on a table behind me. Sit in a chair and look at a point on the wall, be sure there aren't any screens or clocks in your field of vision to distract you.
Once you are sitting looking at the point on the wall let yourself be present and not thinking about anything in the past or the future. The first two or three times you try this it will feel like the longest 20 minutes of your life and you will find yourself constantly thinking of chores, imagining interactions, and berating yourself for thinking. Don't judge yourself and don't "try" to not think. Newbies are often told that if they really need to focus on something, to focus on their breathing.
Normally when you have a thought your mind seizes on the thought like a shark seizes on its dinner. Rather, be like the stone at the bottom of the sea and the thought is like a jellyfish. The thought appears, you are aware of the thought, but you don't engage it, you just let it drift by.