Conduction is transfer of heat from one substance to another through direct contact. When you apply heat to a substance, it agitates the molecules closest to the heat source and raises their temperature. The highly agitated "hotter" molecules will collide with the "calmer" lower-temperature molecules farther from the heat source, with a net transfer of heat energy from higher-temperature molecule to lower-temperature molecule. This process continues from molecule to molecule until all molecules of the substance are at the same temperature. If the heated substance is placed in contact with a cold substance, heat will flow from the agitated molecules of the hot substance to the calmer molecules of the cold substance, agitating them in turn and raising their temperature.
Convection transfers heat from a hot place to a cold place by the circulating motion of a fluid such as air or water. When a fluid is heated, it expands and becomes less dense than the fluid around it, causing the heated fluid to rise. As the heated fluid rises, it creates a low-pressure area that pulls cooler fluid down to the heat source to replace the rising heated fluid. The cooler fluid gets hot and rises, pulling down the previously heated fluid that now has lost its heat to the environment. This cycle forms a convection current that continues to flow until all parts of the fluid are at the same temperature.
Radiation transfers heat by emission of electromagnetic radiation into the environment, cooling the emitting body and warming the environment. The sun warms and lights the Earth though emission of radiation. Heat moves from the interior to the surface of the emitting object by conduction or convection, and then is radiated into the environment. The Stephen-Boltzmann Law says the radiating power of a hot object is a function of its radiating area, the radiator's temperature and the ambient temperature of the environment. A radiating hot object will continue to radiate heat until it and the environment reach the same temperature.
Left to itself, heat won't flow from a cold area to a hot one. But this reverse heat flow can be forced to happen. In nature, convection currents pull fluids from cool areas to hot ones. Humans can reverse heat flow by applying work to a heat-transfer system, and do so all the time with "heat engines" such as heat pumps and refrigeration systems. These devices use a refrigerant liquid compressed under power and forced to condense on the hot side of the device, causing it to give up its heat. Then it's passed to the cold side, where it's forced to evaporate, which extracts heat from the cold side.