The most common ways to transfer heat are conduction and convection. Conduction is heat transfer through mollecular collision. The slower speed particles, or colder particles will increase their kinetic energy after being hit. The capacity of a material transmitting heat by conduction is measured on it's thermal conductivity. A simple example is having a metal, if one edge of the metal is near a fireplace, after a short time all the metal will become hot. This is a phenomenon of conductivity.
Convection is usually associated with liquids and gases and happens when this hot molecules travel away from the source, the fluid becomes less dense and goes up, carrying the thermal energy along. An example is a radiator that warms the air and the hot air goes up cyclically