More Confusing Word Pairs (and Triplets)...

...with thanks to Christopher Orr for his suggestions.

THEY'RE, THERE, THEIR

They're is a contraction (short form) of "they are." The apostrophe indicates where the letter a has been left out.
They're coming!
They're still right where you put them.

There is a preposition, a word that indicates a relationship to place. It is the opposite of "here" and the answer to "where?".
Where's baby's nose? Yes, good! It's right there.
Here and there, a star poked out of the cloudy night sky.

You can also make a contraction between "there is", which becomes "there's". The apostrophe indicates the deleted letter i.
There's nothing wrong with that plan.
There's only one correct solution to each puzzle.

Their(s) is the possessive form of "they":
Our property ends here; past this point it's theirs.
Their cat keeps manacing the birds at my feeder.
It isn't any of their business.
It isn't any business of theirs.

DIE AND DYE

Very confusing! Dying and died are forms of the verb, to die:
He prayed as he lay dying.
The autumn leaves are dying.
Day is dying in the west.
She died six years ago in an auto accident.

Dyeing and dyed are forms of the verb, to dye, meaning to change the color.
She stopped dyeing her gray hair black.
He wore a tie-dyed tee-shirt.

I don't even know what die means as applied to a machine, as in die-cast. Maybe somebody else can enlighten us in its correct usage.

(Note: fly and flying, cry and crying, but flier and town crier.)

BEAR and BARE

Bear is either a large, furry carnivore or else a verb meaning all sorts of things, such as to carry, to endure, to yield fruit, to give birth, etc.
We must try to bear it bravely.
Love bears all things, believes all things, hopes all things.
How are you bearing up?
This tree bears the sweetest apples you ever tasted.
This is a load-bearing wall.
He bore his grief for the rest of his short life.
They have borne for too long the occupation of their land by foreigners.

Bare can be a descriptive word (adjective) meaning uncovered.
The bare branches clutched at the winter clouds.
This is just a bare-bones sketch; we can fill in details later.
What is so cute as a baby's bare bottom?

Or "bare" can be a verb, meaning to uncover.
The vicious dog bared his teeth. (Uncovered them by opening his mouth)
The assassin bared his knife. (Took is out of its sheath)

The confusion creeps in when we consider that "bare" is also an antique past tense of "bear," used where we today would use "bore."
He bare our sorrows.
And she bare a son and called his name Seth.
But except when we are reading Shakespeare or the King James Bible, we don't have to worry about this one. It's obsolete.

WHO and WHOM

Whom is always the object of a verb, the done-unto. Use it wherever you would use "him":
Whom do you trust? (Do you trust him?)
Whom shall we invite? (Shall we invite him?)

Whom can also be an indirect object; always say to whom, for whom, from whom, by whom. Again, you can tell by substituting "him" and seeing if that works:
Praise God from Whom all blessings flow. (From Him all blessings flow.)
To Whom are due all glory, praise, and honor... (to Him are due...)
For whom will you vote? (Will you vote for him?)
...in Whom we live and move and have our being... (In Him we live and move...)

Who is always the subject of a sentence or of a phrase. It's what or who is doing whatever is being done. It stands for "he" rather than "him":
Who is coming to the party? (He is coming to the party.)
Who knows? (He knows.)

Where it gets confusing is when you have a more complex sentence, such as, I will give it to (whoever? whomever?) will take it. What we have to remember here is that every single verb in the whole world has to have a subject. That is, someone or something has to be doing it. In this sentence, the subject of "will give" is "I". I will give it. And the subject of "will take" is whoever, not whomever. He, not him, will take. Whoever, not whomever, will take. Whom is always an object, a done-unto, never a subject, never the doer.
I don't know who used my credit card. ("Who" is the subject of "used".)
She doesn't care who knows about her past. ("Who" is the subject of "knows".)
He wondered who was knocking at the door. ("Who" is the subject of "knocking".)
We will welcome anyone who comes. ("Who" is the subject of "comes".)

In each of these sentences, the entire second phrase, "who used my credit card", "who knows about her past", etc., is the object of the first verb in the sentence. But within that object phrase, each verb still has to have a subject, a doer of the action. "Who", in each of these examples, is the subject of the second verb. "Who" rather than "whom" is the proper form for a subject.

As this post is already long, I'll put the other things people have suggested in another post.