verb forms - Should I use the past tense with did?

Should I use the past tense with did? For example, I was to say:

The important question is: Did they knew what it means or not?

Or should I say:

The important question is: Did they know what it means or not?

In other words: Should I use past tense with did?

I looked at this:

Explanation of "did was [verb]" structure

but it didn't really answer my question.

Answer

Generally speaking, only the first verb in each clause is finite:

They knew what it meant.

Here, know is the finite verb. It changes form to agree with the subject (I know, she knows) and to indicate tense (They know, they knew).

To turn this into a question, we need to apply Subject-Auxiliary Inversion. But to do that, we need an auxiliary, so we add the dummy auxiliary do:

They did know what it meant.

Did they know what it meant?　　←　did and they are inverted

Now do is the finite verb. It changes form to agree with the subject (I do, she does) and to indicate tense (They do, they did). The second verb, know, is non-finite and does not change form.

*Did they knew has two finite verbs and is ungrammatical.