You can start a fire by rubbing sticks together - wood is the fuel, the action of rubbing generates heat and oxygen is all around us. Oxidation is simply the reaction of anything with oxygen. A fuel may be a solid, a liquid or a gas, but combustion will only occur when the fuel is in the form of a vapour - when you light a match it is not the solid wood that is burning but the vapours given off as the wood decomposes in the heat. Soild and liquid fuels must have heat applied to them to vapourise before they can burn. Gases are of course already in vapour form.
Heat travels from regions of high temperature to low temperature.
This only occurs in liquids and gases. When the fluid is heated it expands and becomes less dense. This is heated up by the heat source, rises, and so on. If we are dealing with air in a building, hot air may rise up a stairwell or ventilation duct and then encounter a suitable fuel and fire may start. The energy from a heat source can be transmitted to objects at some distance away by radiation - similar to light waves, but with longer wavelengths.