How are free radicals generated?

Answer 1

The simplest answer might be that free radicals are generated when a covalent bond is broken in such a way that each atom involved in the bond keeps one of the electrons from the bond. This results with each atom of the bond with an unpaired electron making them form free radicals. There are various ways in which free radicals can form (heat, uv light, ionizing radiation, etc.).

Answer 2

It depends on the structure and the conditions at hand.

In sophomore organic chemistry classes, radicals are typically taught to be generated via "homolysis" or homolytic cleavage. Basically, light or heat breaks a sigma (single) bond, generating two radicals. Classic example is the homolysis of Br₂ in free-radical bromination reactions.

But radicals themselves can be used to generate other radicals. During propagation steps, Br radicals can "abstract" hydrogens from C(sp³)-H bonds to obtain carbon-centered radicals, and this can further go on to attach Br via interaction of the carbon radical with Br₂. So I'd say that's the minimum you would have to know for a class.

For some FYI, modern day methods utilize visible light or electricity to further reduce (add an additional electron) to species, forming radical anion species that fragment into an anion and radical. This process is known as mesolysis or mesolytic cleavage, and it's another clever way to generate radicals.

Hope this helps!