I think 'neutron-rich' and 'neutron deficient' just refers to the neutron : proton ratio of the nuclei.
If there were much more neutrons than protons in a nuclei, then it would most likely be unstable and also be considered as 'neutron-rich' (due to the excess of neutrons). You can probably produce 'neutron-rich' isotopes in a nuclear reactor by bombarding your nuclei with a neutron. An example of this could be when you bombard iron-58 with a neutron.
Iron-58 would essentially 'capture' this neutron and become neutron-rich Iron-59. This would be unstable due to the excess of neutrons (although it has a rather long half-life of 45 days or something), resulting in Iron-59 slowly undergoing beta decay to become Cobalt-59.
If something was neutron-deficient, it would mean that there is an excess of protons within the nuclei instead. This could be done through light nuclei bombardment in a linear accelerator or a cyclotron. I can't think of a specific example off the top of my head but maybe bombarding something with a couple of protons would make your nuclei neutron-deficient.
I guess a way to distinguish if something is neutron-rich/deficient or not is to identify whether it undergoes some sort of beta decay as that would indicate that it doesn't have a very stable neutron : proton ratio.
Alternatively, you could just use the periodic table to identify the most common isotope of an element (provided it has an atomic number less than 83) and from that you can calculate the number of neutrons required for it to be stable. For example, Carbon has a standard atomic weight of 12.01 - this would meant that the most common stable isotope of Carbon would be Carbon-12 which has 6 neutrons. Therefore, I guess any Carbon nuclei with more or less than 6 neutrons would make the carbon nuclei neutron rich or deficient.
Oh and if you're wondering why the above method was only limited to elements with an atomic number less than 83, it's essentially due to the fact that anything after bismuth (atomic number of 83) is considered unstable.
Hope my information was correct and that it made sense!