How do I start studying chemical nomenclature?
Chemical nomenclature is mixture of historical traits, empirical knowledge and little bit of systematics.
And as you mentioned, it is exhaustive to learn all at once. 

To understand the nomenclature, you must understand the systems themselves. Because it's their structure and reactivity which is reflected in the name. 

This makes an unfortunate cyclic dependency. To start studying any given chemistry branch, you must know its language. But without knowing the science behind, the language does not make sense. It's like that and you probably cannot do anything about it, just cut this circle and crunch through the nomenclature. It will start to make sense, once you get sufficiently deep. Additionally, the "why" is good indicator. Once you have enough knowledge to understand the answer why it is named so, than you can probably answer yourself.