The basic form of an English sentence is:

where “NP” is a Noun Phrase (the subject), “Aux” is the Auxiliary Verb(s), and “VP” is the Verb Phrase.  Here I discuss the structure and function of the Auxiliary Verb(s), and related topics.

Auxiliary Verbs must always come in this order in English.  Tense is required in a complete sentence of English; the other Auxiliaries are optional. (I show that these other Auxiliaries are optional by putting them in parentheses).

There are two Tenses in English: past and present.  Despite what many English speakers (and English teachers) may tell you, English does not have a future tense.  Of course we can talk about the future in English, but not by using a tense; instead, we must use an entirely new, second word – the Modal Auxiliary "will" – to refer to the future.  A tense is a grammatical item which gets attached to the verb, and (at least sometimes) changes the sound of the verb. Example:
 
 

But there is no way of changing the sound of "run" to mean "John runs tomorrow"; instead we must use "will," and leave the verb "run" unchanged.

When the tense is 'turned off' in English, it is pronouned "to".  So, for example, "to run" is the verb "run" with a ‘zero’ tense attached.  A verb with this ‘zero’ tense is called an infinitive; “to run” is the infinitive of “run”.

 We can divide verbs into two families – the Regular Verbs, and the Irregular Verbs – depending on how they react to Past Tense.  With a regular verb, the Past Tense will be that verb, plus “-ed” at the end.  Here are some regular verbs:
 
 

An irregular verb does not follow the “-ed” rule for Past Tense.  The sound of an irregular verb with Past Tense is different for each irregular verb (that’s why they’re irregular).  You can’t use a rule to predict the Past Tense of an irregular verb; you simply have to memorize it.  Here are some irregular verbs:
 
 

Modals provide further evidence that there are only two Tenses in English: that explains why there are two forms of every modal (May/Might, Can/Could, Shall/Should, Will/Would).  Someone who thought there were more than two Tenses in English would have a harder time explaining why the Modal Auxiliary Verbs pair up like this.

Two more points about Modals and Tense:

    (1) Unlike other verbs, Modals never show up without Tense – there is no infinitive form of a Modal.  By contrast, a regular (main) verb can show up without tense in a sentence (as long as that sentence is part of a bigger sentence):

win:    I want [John to win the race]
rake:  I want [John to rake the leaves]

I want [John to have written a book by then]
I want [John to be writing his second novel by then]

    (2) When Tense is attached to a regular (main) verb, or to the Auxiliaries “Have-en” and “Be-ing,” the Tense makes the verb talk about time (past or present).  However, when Tense is attached to a Modal verb, it does not always refer to time (past or present); Tense on a Modal has different and unusual meanings.

Main Verb: write
“John writes”

Have-en:
"John has written"

Be-ing:
"John is writing"

Note: the “-en” in “Have-en” is not always pronounced as “en”; I just use “-en” here as a symbol of  the little affix that goes with “Have”.  What the “-en” sounds like depends on what kind of verb the “-en” attaches itself to.

(i) With Regular Verbs, “-en” will sound the same as Past Tense (“ed”).

(ii) With some Irregular Verbs, “-en” actually does sound like “en”

 
 (iii) With other Irregular Verbs, “-en” is pronounced as a change in the verb itself.  This may or may not be the same change that Past Tense makes (though usually it is).

(iv) With some Irregular Verbs, “-en” makes no sound at all.

However, the “-ing” in “Be-ing” is always pronounced “ing,” whether the verb is regular or irregular:

walk:  “John is walking down the street”
paint: “John is painting a picture”
bake: “John is baking a cake”
write: “John is writing a letter”
see: “John is seeing a movie”
drive: “John is driving a truck”
swim: “John is swimming in the pool”
ring: “John is ringing the bell”
feel: “John is feeling sad today”
sleep: “John is sleeping now”
run: “John is running in the marathon”

Present:
John (present+write)
"John writes"

Past:
John (past+write)
"John wrote"

Present+Modal ("May")
John (present+may) write
"John may write"

Past+Modal ("May")
John (past+may) write
"John might write"

Present+Modal ("Can")
John (present+can) write
"John can write"

Past+Modal ("Can")
John (past+can) write
"John could write"

Present+Modal ("Shall")
John (present+shall) write
"John shall write"

Past+Modal ("Shall")
John (past+shall) write
"John should write"

Present+Modal ("Will")
John (present+will) write
"John will write"

Past+Modal ("Will")
John (past+will) write
"John would write"

Present+Have-en
John present+have write+en
"John has written"

Past+Have-en
John past+have write+en
"John had written"

Present+Be-ing
John present+be write+ing
"John is writing"

Past+Be-ing
John past+be write+ing
"John was writing"

Present, Modal, Have-en
John present+will have write+en
"John will have written"

Past, Modal, Have-en
John past+will have write+en
"John would have written"

Present, Modal, Be-ing
John present+will be write+ing
"John will be writing"

Past, Modal, Be-ing
John past+will be write+ing
"John would be writing"

Present, Modal, Have-en, Be-ing
John present+will have be+en write+ing
"John will have been writing"

Past, Modal, Have-en, Be-ing
John past+will have be+en write+ing
"John would have been writing"

Remember the order of the Auxiliary Verbs in English:

Now here is a rule for making "Yes-No" Questions in English (questions which have either a "yes" or "no" answer).
 

Yes-No Question Rule:
Move Tense, and the first Auxiliary Verb after it (if any) to the front of the sentence

1.
I present+will have write+en the letter by then
“I will have written the letter by then”

Q1.
Present+will I ____ have write+en the letter by then
“Will I  have written the letter by then?”

2.
She present+have write+en the letter
“She had written the letter”

Q2.
Present+have she ____ write+en the letter
“Had she written the letter?”

3.
John past+have be+en write+ing a letter
“John had been writing a letter”

Q3.
Past+have John ____ be+en write+ing a letter
“Had John  been writing a letter?”

But what if there is only Tense, and no other Auxiliary verb?  Then Tense gets moved to the front of the sentence all by itself.  But wait: that's no good.  Tense is an affix.  It can't stand all by itself; it needs to attach itself to a verb, to its right.  So what do we do then?

4.
John present write many letters
“John writes many letters”

Q4.
Present John ___ write letters
“Does John write many letters?”

5.
John past write many letters
“John wrote many letters”

Q5.
past John ___ write many letters
“Did John write many letters?”

This is another rule of English: if Tense gets left all alone, with no verb next to it to attach itself to, then put in the empty verb "Do".  This rule is called “Do” Support.  (English is the only language which has this rule.)

“Do” Support Rule:
If Tense has no Verb to its right to attach itself to, then put "Do" to the right of Tense.

Next we build a rule for negations (denials, using the word "not").

Negation Rule:
Put "not" after Tense, and the first Auxiliary Verb after it (if any).

I present+will have write+en a letter
"I will have written a letter"
"I will not have written a letter"

I past+have write+en the letter
"I had written the letter"
"I had not written the letter"

I past+be write+ing a letter
"I was writing a letter"
"I was not writing a letter"

I past+have be+en write+ing a letter
"I had been writing a letter"
"I had not been writing a letter"

And notice: if Tense is the only Auxiliary in the sentence, then according to the Negation Rule, "not" goes right after Tense.  But then Tense will have no verb on its right, to attach itself to.  So the word "do" must be inserted after Tense, as required by the "Do” Support rule.
 

John past+write the letters
"John wrote the letters"

John past not write letters
John past+do not write the letters
"John did not write the letters"

Next we build a rule for 'Tag Questions'.

A Tag Question is a little Yes-No question, added to the end of a statement.  Here are some examples of Tag Questions:

You will eat some ice cream, won't you?
John hasn't been to France before, has he?
John is writing the letter, isn't he?

(i) Put in the Tense of the statement, and the first Aux verb after it (if any)

(ii) If the statement is affirmative (positive), make the Tag Question negative (containing the contraction of the word "not": "n't"); if the statement was already negative, make the Tag Question Affirmative (without the “n’t”).

(iii) Put in the pronoun version of the subject.  ("You" is already a pronoun; "John" is not a pronoun, so we use "he".)

 Take the first sentence as an example:

"You will eat some ice cream"
You present+will eat some ice cream
(i) You present+will eat some ice cream, present+will
(ii) You present+will eat some ice cream, present+will+"n't"
(iii) You present+will eat some ice cream, present+will+"n't" you
"You will eat some ice cream, won't you?"

"You like ice cream"
You present+like ice cream
(i) You present+like ice cream, present
(ii) You present+like ice cream, present "n't"
(iii) You present+like ice cream, present "n't" you

(iv) You present+like ice cream, present+do+"n't" you
"You like ice cream, don't you?"

A “Wh”-Question is a question using the “Wh”-phrases who, what, when, where, why, which, whose, and how.  ("How" doesn’t actually begin with the letters “wh,” but it still belongs in that family of words.)

Here are some examples:

Who are you talking to?
What had he written in his letter?
When do you get off work?
Where have you put the spray bottle?
Why are you writing him a letter?
Which brush do you like better?
Whose brush are you using now?
How will he find you?

Consider a simple example:

What was John eating for breakfast?

John was eating what for breakfast.

The main exception to this is the Echo Question, used when we either (i) didn’t hear what the speaker said, and are asking them to repeat it, or (ii) are expressing surprise at what the speaker said.  Here are some Echo Questions:

 1. John was eating [mmrmhhmr] for breakfast
 E1. John was eating what for breakfast?  (didn’t hear, asking speaker to repeat)

 2. John was eating a peanut-butter and sardine sandwich for breakfast
 E2. John was eating WHAT for breakfast!? (expressing surprise)

If I really want to ask about John’s breakfast, I use an ordinary “Wh”-Question, not an Echo Question.  To build a “Wh”-Question, I do two things:

 (i) Apply the “Yes-No” Question Rule
 (ii) Move the “Wh”-phrase to the front of the question

“John was eating what for breakfast.”
John past+be eat+ing what for breakfast

Past+be John ____ eat+ing what for breakfast  (“Yes-No” Question Rule)
What past+be John ____ eat+ing ____ for breakfast  (“Wh”-Movement)
“What was John eating for breakfast?”

 Try another example:

 “John likes talking with who”
 John present like talking with who

 present John ____ like talking with who  (“Yes-No” Question Rule)
 present+do John ____ like talking with who  (“Do” Support Rule)
 who present+do John like talking with ____ (“Wh”-Movement)
 “Who does John like talking to?”

(Here we needed “Do” Support as well, because the “Yes-No” Question Rule left Tense without any verb to attach itself to.)
 

Once you understand how to make “Wh”-Questions, it’s easy to make Relative Clauses.  Relative Clauses are small sentences (“clauses”) that describe something, the same way an Adjective Phrase does.

Example:

John is a popular guy
(“Popular” is an Adjective Phrase – it tells us what kind of guy he is)

John is a guy who everyone will like
(“Who everyone will like” is a Relative Clause – it tells us what kind of guy he is.)

The only difference between Relative Clauses and ordinary “Wh”-Questions is this: Relative Clauses do not use the “Yes-No” Question Rule, but “Wh”-Questions do use the “Yes-No” Question Rule.

“Wh”-Question Rule:
 (i) Apply the “Yes-No” Question Rule
 (ii) Move the “Wh”-phrase to the front of the question

Relative Clause Rule:
 Move the “Wh”-phrase to the front of the relative clause

 So we start with this (Echo Question) sentence:
 

 Everyone will like who

To make a Relative Clause from this, we simply move the “Wh”-phrase to the front of the sentence:
 

 Who everyone will like ____

But to make a complete “Wh”-Question, we must also apply the “Yes-No” Question Rule:
 

 Who will everyone ____ like ______
 “Who will everyone like?”