There are 4 ways in which electrons are emitted from the conductor.
i. Thermionic emission
ii. Electric field electron emission
iii. Photoelectric emission
iv. Secondary emission
In thermionic emission large amount of external energy in the form of heat is supplied to release free electrons from the metal.
In electric field electron emission, electrons are emitted from the metal surface when the metals are placed in a very strong electric field.
During photoelectric emission, light is absorbed by the metals and this provides energy to the valence electrons which break their bond with the parent atom and which are then released from the atom.
Valence electrons do have some kinetic energy, but they don't have enough energy to escape from the atom. During secondary emission, a high-speed electron is bombarded with an atom, which provides the energy for the valence electrons to break their bonds with their parent atom which are then released from the atom.