Conduction: conduction is the transfer of heat due to direct contact between two mediums, or between two parts of the same medium at different temperature. In conduction, the particles of the hotter medium vibrate faster than the particles of the colder medium, so the particles of the first medium transfer kinetic energy (by means of collisions) to the particles of the second medium, until when the two mediums reach the same temperature.
Convection: convection is the transfer of heat due to movement of masses of molecules in fluid. Convection occurs when a fluid is heated by an external source: the region of the fluid closer to the source gets warmer, so it expands and becomes less dense; as a consequence, it rises while the colder, denser regions of the fluid sink towards the source of heat. The process then continues forming the so-called "convective current", until the source of heat is turned off.
Radiation: radiation is the transfer of heat through electromagnetic radiation. Electromagnetic waves consist of oscillating electric and magnetic fields, which carry energy through space. Every object emits electromagnetic radiation, so every object transfer heat by radiation. This is the only method of heat transfer that does not require a medium to occur, since electromagnetic radiation can travel in vacuuum also.