A cup of hot tea can lose heat via conduction, convection, thermal radiation, and evaporation. Let's look at each one individually.
Thermal radiation is the loss of heat from a solid object into the atmosphere via the release of electromagnetic radiation. So the hot outer edge of the teacup will lose its heat to the surrounding air via thermal radiation.
Conduction is the movement of heat along a gradient within a solid. So the inner part of the teacup against the hot liquid will transfer that heat to the cooler outer part of the teacup (where it will be lost via thermal radiation).
Convection is the movement of molecules of a liquid or gas within itself. So hot molecules of tea in the middle of the drink will eventually make their way to the outer part of the drink near the teacup where they will lose their heat.
Finally, evaporation is the conversion of liquid water to gaseous water. Since gaseous water is in a higher energy state than liquid water, energy is required for the water to evaporate. The energy in this case comes from the heat of the drink. As energy is lost due to evapration, the drink slowly cools as a result. This is the reason that a container of a highly volatile liquid always feels cool to the touch since it absorbs the heat from your fingers to evaporate the liquid.