How could the campfire

warm things by conduction and radiation?

The heat can tranfer both directly and through electromagnetic waves.

Radiation is what occurs when energy is transmitted or emission of energy through the space or in the form of waves. This includes: electromagnetic radiation, such as radio waves, microwaves, infrared, visible light, ultraviolet, x-rays, and gamma radiation

Conduction is a a more so physical contact situation but if connection to the ground is made then the heat can transfer into the ground and proceed to spread into a wider vicinity warming the general area around it in a more physical manner.