When you have some acronyms and want to tell others what they mean or stand for, are the articles necessary? If so, is that because the articles are the parts of the grammatically constructed sentences? I am not sure whether the acronym here is correct.

CDC means/stands for the Center for Disease Control

CDC means/stands for 'Center for Disease Control'

CDC means/stands for the 'Center for Disease Control'

CDC means/stands for 'the Center for Disease Control'

Some acronyms have THEs as parts of their names and some do not, I think. How do we know whether THEs are attached to their names? Look at the prints?
Yes, I think you need to go back and research whether or not "the" is part of the organization's name. Let Google be your partner in this. In most cases, I'd recommend using the "the" because it will sound more natural.

I note the CDC refers to itself as CDC, not "the CDC," in running text, but spelled out, calls itself "The Centers for Disease Control and Prevention."

As a side note, note that it's Centers. Most people don't notice that Centers is plural.

Please note that CDC is not an acronym. It's an abbreviation.

An acronym is an abbreviation that is pronounced as a word, eg NATO (we say naytow).

Best wishes, Clive