Combustion is a chemical reaction. When a chemical reaction takes place, what happens on the atomic level is that chemical bonds between atoms are broken and new bonds are formed between different atoms.
In order for molecules to react they must be moving fast enough to have enough collisions. Collisions only result in a reaction if the molecules collide with enough energy and in the proper orientation. In the case of methane combusting, some energy must be provided to initiate the reaction at normal temperatures. This is called the activation energy. Matches, lighters and electronic igniters are common sources of activation energy.
Here's the balanced equation for the combustion of methane:
` CH_4 + 2 O_2 -> CO_2 + 2H_2O`
Each molecule of methane that reacts requires 2 molecules of oxygen. The chemical bonds are broken and reformed in steps and there are intermediate structures formed that go away, but for the sake of simplicity we'll look at it as though all of the reactant bonds break then all of the product bonds form.
Four carbon-hydrogen bonds are broken in methane, producing a carbon atom and 4 hydrogen atoms. An oxygen-oxygen double bond breaks in each of the oxygen molecules, giving us 4 oxygen atoms.
Two molecules of water are formed when each oxygen forms new bonds to two hydrogen atoms. A carbon dioxide molecule forms when the carbon atom forms double bonds with two different oxygen atoms.
There are the same number of each type of atom in the products as in the reactants: 1 carbon, 4 hydrogens and 4 oxygens. Atoms are neither created nor destroyed, they're just rearranged into different molecules.
Energy is released when new bonds are formed. In this chemical reaction the amount of energy released is greater than the amount of energy absorbed to break the original bonds, so the reaction is exothermic (releases energy).