How does energy move in the atmosphere?
Advection, convection, radiation, conduction and latent heat changed into sensible heat.
Advection is warm or cold air moving horizontally. This is often seen as a warm front or cold front.
Convection is the vertical transfer of heat by air rising due to unequal heating of the surface of the Earth (air over a field of soil is going to heat up faster than a snow covered field and this will cause that air to rise).
Radiation is the transfer of energy in waves. The warm Earth is radiating infrared radiation and that heats the air.
Conduction is the heating of things through direct contact. The air immediately in contact with the ground is heating through conduction. The air immediately touching warmer air is heated the same way. Since this only heats the atmosphere that is directly in contact with the heat source, it contributes least to energy transfer.
Finally, when water changes state it stores energy as latent heat. Think of a pot of boiling water on an element. The element continues to add heat but the water never gets hotter than the boiling point. Where does the extra energy go? Into the actual water molecules themselves. This is not heat you can feel (sensible heat), it is hidden in the water molecule (latent comes from a latin word base that means hidden).
When the water vapor changes back into liquid (condensation as occurs in cloud formation) it releases the latent heat that was stored as vapor as sensible heat that you can feel.