Oxygen Avilablity
The principle limiting factor in most day-to-day combustion reactions is the availability of oxygen. By using bellows or other pumping devices, you can introduce more air into the reaction, increasing the concentration of available oxygen and speeding the combustion. When there is sufficient oxygen to combine with the fuel, the flame burns very cleanly, often burning blue--or even clear--leaving minimal soot. When insufficient oxygen is available, the flame burns a dull yellow and leaves behind black marks where carbon not joined to the oxygen is carried in the flame and deposited.
Concentration and Surface Area
As well as increasing oxygen availability, the rate of reaction will be governed by the fuel availability. You can increase this by mixing fuel with another substance, using a greater concentration of the flammable ingredient. You also can increase it by breaking the reactant down into smaller pieces. This raises the surface area of the reactant, increasing the rate at which oxygen and the fuel can interact.
Increasing Pressure
If the reaction occurs in a sealed or partially sealed environment, you can increase the reaction rate by raising the pressure in which it occurs. Do this by decreasing the size of the environment or introducing greater volumes of air and reactants. This increases the number of collisions that occur between reactants and oxygen, causing more reactions per second.
Catalysts
A catalyst is a substance introduced into the reaction which speeds up the rate of the reaction without being used up in the process. Generally, the catalyst works by offering a surface where the substances can interact. Having a surface to react on makes it far more likely for particular atoms of oxygen to react with particular atoms of the reactant, thus increasing the rate of reaction.