Conduction is the transfer of heat within a substance, molecule by molecule. So if you heat up the bottom of a solid; (i.e. a frying pan)the bottom layer of particles gain more kinetic energy, and transfer kinetic energy to the next lay, which in turn transfer energy to the layer above, and so on. As a whole, the heat travels through the solid from the heat source spreading out to the edges of the object.
Convection is the heat transfer by the mass movement of a fluid in a vertical (up/down) direction. Warm water is less dense than cold water, making cold water heavier than warm water. so if you heat up a beaker of water from the base, the warm water molecules at the bottom (heated by conduction) rise up to the surface, and the cooler molecules from the surface fall down to the bottom. These cool molecules are now closer to the heat source and so rise, and the previously hotter molecules fall back down to the base to, in turn, be heated and rise again, and so. This process of rising and falling creates a current in the fluid, which can be called a Convection Current.
Radiation is the emission of energy as waves rather than through particles as before. These waves are called Electromagnetic Waves, because the energy travels in a combination of electric and magnetic waves. This energy in these waves is released when these waves are absorbed by an object, for example, energy travelling from the sun to your skin (as infra-red waves). You can feel your skin getting warmer as energy is absorbed.
The image below shows all three concepts, in a way that should aid your understanding