commercial radioisotopes are generally produced in nuclear reactors. Suitable target nuclei are placed in the reactor core and bombarded with neutrons until the required radioisotope is produced (eg Co-60 is produced from Co-59). NB; these radioisotopes need not be transuranic elements.
Also, radioisotopes may be produced as a direct product of nuclear fission (when a heavy nuclei captures a neutron, then breaks apart into similarly-sized fragments). For example, the 'mother' or precursor of technetium-99m (molybdenum something? i can't remember...) is a product of uranium fission.