Learn English – a day of, or the day of

As far as I know, the article the comes from the old English word for that (if something has a the in front of it, you can point at it). So, you can kind of mentally substitute the with that (or those for things that are plural) and if the whole thing still makes sense, then the usage is most likely correct. The indefinite article a/an, again, comes from the old English word for one. I usually think of it like this:

Volvo is a car. It is a car because it is just one of many possible cars that exist.

or

Volvo is a car. It is a car because it is one example of the nebulous idea of car.

Another example:

I'm gonna buy a car. I'm gonna buy just one out of many cars that exist.

With the, I think, we will typically be able to add some very specific information about the object we are talking about. For example:

I saw the man again. (The man that we met yesterday and his name was John.)

Where are the kids, honey? (The kids that are named Jimmy and Bobby because they are our sons.)

Compare that with examples using a:

I saw a man again. (maybe in my dream) (just a man, one of the class man)

What do kids like most of all, honey? (just kids in general, not our children or our future children)

I suppose if you wanted to say something about the "20s decade" of any century, you could say, "I love 20s" or "20s are periods of change" or whatever. But it's such an unlikely thing to say, I'd be surprised if you could find an example.

But to take a more likely analogy, suppose you were talking about the basement of a building. If you were talking about the basement of one particular building, you might say, "I clean the basement." You use "the" because you are talking about one particular basement. But if you wanted to talk about the basement of any building, you could say, "I clean basements." Now there's no article because we are talking about basements in general and not one particular basement.

As "the 20s" would normally be understood to mean "the 1920s", we are talking about one particular period of time, so you use the singular and the definite article. (I suppose if someone in 1840 talked about "the 20s", he presumably meant "the 1820s", and if 30 years from now people talk about "the 20s", they'll probably mean "the 2020s", unless the context makes clear that you're talking about some other century.)

Note that regardless of whether you are talking about a specific thing or a general thing, if you use the singular, you need an article, a possessive, the number "one", or one of a few other special pronouns. Like if we are searching for your lost dog, I might say, "I see the dog" or "I see your dog." If we are wandering about and see an unknown dog, I would say, "I see a dog." It would never be correct to say, "I see dog." (Well, you could say "I see Dog" if you are talking about Dog the Bounty Hunter, a person named "Dog". But then it's a proper noun.)

As Mick notes in his comment, you could use "20s" without an article if you were using it as an adjective rather than a noun, and the noun in question does not call for an article. Which would usually mean that it is either plural or uncountable. "I like 20s music" (uncountable) or "There were several 20s cars in the antique car show" (plural).