You always need an auxiliary verb for a question. You can't have a question without an auxiliary verb.
For the purposes of making questions, auxiliary verbs are: have, do, be, and all the modal verbs. Note that "have" can sometimes be a main verb (when it means "possess" or "must"), and "do" can also be a main verb. As a rule of thumb, it's an auxiliary if it's only there for the grammar, but a main verb if it describes an action ("do your homework", for example, describes the action of completing one's homework).
To make a question, all you really need to do is to swap subject and auxiliary verb, like this:
It is raining. -> Is it raining?
Pete has made a cake. -> Has Pete made a cake?
Piedro is Spanish. -> Is Piedro Spanish?
Sue can see me. -> Can Sue see me?
Note that "be" is a special case. But in all the other sentences, the subject comes before the main verb. This is how the subject is identified in modern English -- it must come before the main verb.
But with the simple past and simple present, we don't have an auxiliary verb, so there's nothing to swap the subject with:
Mary works as a teacher. ->
We can't swap subject and main verb, because that would put the subject after the main verb, and we're not allowed to do that. (If they've read Shakespeare, you have to explain that the rules were different in Shakespeare's day.)
To the rescue, wearing its "Superverb" costume, the all-purpose auxiliary verb "do" leaps in to save the day. It doesn't change the meaning or the tense, but it helps us ask questions. Now we can change the sentence around to make a question, leaving the subject and main verb in the correct positions:
Does Mary work as a teacher?
And there it is -- Superverb saves the day!
A similar principle applies to making negative sentences: we do this by putting "not" after the auxiliary verb, but when the sentence has no auxiliary verb, Superverb has to leap in and save the day:
Sue can't see me.
Mary doesn't work as a teacher.