Fire is a chemical reaction, often between different chemical compounds or elements, each which has stored energy. That is the science of it. You can study more on how combustion happens in an interactive tutorial from NOVA at www.pbs.org/wgbh/nova/physics/science-fire.html.
But for the beginner think of it this way:
To make fire, you need heat, fuel and oxygen. heat from the friction of two sticks, a match head on a striker, a piece of steel struck against a flint. Fuel is the stuff that burns. When you are making fire, you want a wad of dried moss to 'catch' the first sparks. Blowing on the smoldering sticks or moss causes the hot tinder to burst into flame. At the moment t begins to glow red, add a gentle breeze of a breathe to feed it the oxygen it needs to burn. Have more dried moss and leaves on hand to feed the little flames until you can add small sticks and more oxygen either by fanning the flames or blowing on them.That is the basic street explanation that can be argued but not disproven.
This is the stick method:
You spin the friction making stick back and forth with the dried leaves under the point of friction at the bottom. There are easier ways but this will work.
The bow drill:
This is a little more complicated, in that you must gather some pieces of wood and twine together in one place, but this bow drill method beats rubbing a stick around and around in your hands.
The Fire PloughThe one stick method allows that you rub a stick into a groove in a dried branch or board. surprisingly a palm frond makes a great friction board for this method. It also provides some very fine hairy fibers that will spark quickly as you rub the pointed stick into the branch. Have more dried fibers on hand, they burn quickly.
The magnifying glass method.
The magnifier is held at an angle to the sun until the light becomes a pinpoint on the dried moss, paper or leaves.
Flint and Steel
After you have acquired a piece of steel an any number of shapes or sizes and a piece of flint (a rock) you can make your own fire starter kit in an old Altoids can. Strike the steel against the flint to make sparks over the dried straw or moss, blow and and add fuel.
Magnesium Fire Striker
Don't leave home without one. These are the greatest thing since the invention of the disposable lighter to have on you when you want to make fire. They come in many shapes, weigh next to nothing in the bug out bag and can be found in the camping aisle at Wal Mart or online in any sporting goods store or survival store for $5 - $9 depending on the carry case that comes with it.
To bring Fire making to a close I want to share something I have never seen before but will be trying this weekend!
The Coke and chocolate method !!!!????? Yes, this guy polishes the bottom of a soda can with the chocolate to make a very shiny parabolic mirror.