i was thinking today, there is often debate about how these words are incorrectly interchanged, but ive never actually got a definition. can anyone tell me in what instances you would use either of these?

According to dictionary.com:

The typical usage guide statement about the choice between who and whom says that the choice must be determined by the grammar of the clause within which this pronoun occurs. Who is the appropriate form for the subject of a sentence or clause: Who are you? The voters who elected him have not been disappointed. Whom is the objective form: Whom did you ask? To whom are we obliged for this assistance? This method of selecting the appropriate form is generally characteristic of formal writing and is usually followed in edited prose.

In most speech and writing, however, since who or whom often occurs at the beginning of the sentence or clause, there is a strong tendency to choose who no matter what its function. Even in edited prose, who occurs at least ten times as often as whom, regardless of grammatical function. Only when it directly follows a preposition is whom more likely to occur than who: Mr. Erickson is the man to whom you should address your request.

In natural informal speech, whom is quite rare. Who were you speaking to? is far more likely to occur than the “correct” To whom were you speaking? or Whom were you speaking to? However, the notion that whom is somehow more “correct” or elegant than who leads some speakers to hypercorrect uses of whom: Whom are you? The person whom is in charge has left the office.

Never end a sentence with a preposition...

The easiest way to gauge is by using "to"

Who is that guy?

To whom were you referring?

Who said it, to whom?

A trick you can use to remember when to use each is this:
In each example, can the word who or whom be replaced by he or him? If you can replace it with him, then you should be using whom. If you can replace it with he, then you should be using who.
For example, "Who were you talking with?"
Okay, what can you replace who with in that sentence?
Does "I was talking to he"? No!
"I was talking to him." You are using him, so you should use whom. The example I used "Who were you talking with?" was wrong. It should be "Whom were you talking with."

"Whom do you think is the most beautiful?" Again, wrong. Is her the most beautiful? No. She is the most beautiful.

It should be "Who do you think is the most beautiful?"

If you use she/he, then it's subjective and you use who. If it's her/him, then it's objective and you use whom.

If you can master this, then you're doing well. Hardly anybody knows how to use who and whom.

It's difficult to sort it out in real time while speaking. Even accomplished speakers err on the side of caution and use "who" whenever "whom" is not the absolutely obvious choice. "Who" is acceptable, especially in America, whereas using "whom" incorrectly is never acceptable. It sounds like all those uneducated people who want to sound educated by overcompensating for bad grammar and pronunciation even when it's not bad, and end up just sounding silly.

• "This is just between you and I" instead of "between you and me."
• "Bei-zhing" instead of "Beijing," as though it were French instead of Chinese.
• "I don't know whom I'm supposed to be." (The Clash, "Should I Stay or Should I Go.")
• "Of-ten" instead of "offen" for the word "often."

As François points out, to get it right you often have to deconstruct your sentence and rebuild your subordinate clause with the word order straightened out to determine whether your who/whom is the subject or the object of the clause. You can do that while you're writing but not while you're speaking.Of course you're being facetious.

"What did you blame that lady I saw you getting mad at for?" --> "For what did you blame that lady at whom I saw you getting mad?"

Winston Churchill is often quoted as saying, "This is something up with which I shall not put." This has to be apocryphal, because Churchill of all people would know that "up" is an adverb in that sentence, as it is more often than not. It should be, "This is something with which I shall not put up."

A question that should be asked is when to use "who" instead of "that." In colloquial speech we often say, "The man that I spoke with at the store..." When the referent is a person, we should say, "The man who I spoke with." This is actually a worse grammatical error than using "who" instead of "whom," and far worse than ending the sentence with a preposition, which is not even an error in our language. (Only in Latin, it comes from 19th century English books, which were clumsy and inadvertently humorous translations of Latin textbooks.)

'My Generation,' would never had had the same impact had it been written by The Whom.

Nor would an album entitled "Whose Next."

How about cutting out the 'that' or 'who' in the sentence? Is that incorrect?

e.g. The man I spoke to.

Is it just the speaker being lazy and dropping a word?

I think it depends on what the reference is, ie. on whether it is an object or a person. Example 1: The man that came to fix the fridge. Example 2: The man who married my sister. I don't know how correct it is because I don't know the science behind grammar, but it just seems to sound right.

That's the way I'm thinking about it, too.

That's generally the way I say it when I speak, so I wondered. I cut off quite a few words.

I don't bother with 'I'm' at the start of a sentence quite often. I'll say - Getting a beer. Totally knackered. Going to the shop. - etc. That's me being lazy

If you're just speaking with someone, and depending on how casual the conversation / statement is, you can probably get away with talking in monosyllables, but if you're writing, and again depending on how credible you want to appear, you must use proper grammar and syntax.

I haven't got the style manual memorized, but I see this in writing so it's probably considered correct. Especially in informal usage rather than in a treaty, contract or ordinance. So it's an easy way to be safe; you don't have to figure out whether it should be "who" or "that." No, that's wrong. It's "The man who came to fix the fridge." Your reasoning is correct but your analysis is wrong. In both cases, the reference of the relative pronoun is to the noun "man," not to "fridge" or "sister."Colloquial usage is colloquial, that's why we call it that. But what you're doing can be seen as speaking in sentence fragments that can be interpreted in context.

Why are you walking into the kitchen in your underwear?
[I'm] getting a beer.

But why is your underwear on backwards?
[I'm] totally knackered.

Then why are you fetching your car keys while totally knackered in your underwear, which is on backwards?
[After I finish my beer, I'm] going to the shop. As I say, there's more than credibility to it. In a face to face conversation, much of what you would write in a sentence can go unspoken because it is implied from a visual context, a relationship, your habits, etc.

So what?

It explains why written language has to diverge slightly from spoken language. The rules are stricter because less can be gathered from external context.