Grammar is there to help
The first thing you need to realize is that the rules of grammar are there to help. Following them makes your writing clearer and easier to understand. Not following them runs the risk of confusing the reader or sounding unprofessional.
Your Writing. Your Rules.
That being said, you as an author should not bind yourself 100% to the rules of grammar. Use them, but if your story would be better served by writing something which isn't entirely grammatically correct, do it.
However, make sure that your story would be better served by doing so. Any time you go against the rules of grammar, make sure your story is clearer for it, or the wording is more powerful. If that isn't the case, it might be better to follow the rules of grammar instead.
Okay. So when do the rules of grammar say you should use exclamation marks? According to my handy Abeka Handbook, you should use an exclamation mark to end an exclamatory sentence (literally, a sentence which conveys excitement or passion), or to end an imperative sentence (a command) strongly stated.
Don't do that! Help!
Where should you use an exclamation mark?
Exclamation marks generally go with quotes, that is, the spoken words of people or characters. People/characters exclaim about things all the time, and it's natural to put exclamation marks in. There's no wrong amount when used this way, as long as you use them as they are meant, and only end exclamatory sentences with them.
"I don't want to die!" John cried. "Help us!" Mary shrieked. "That was funny!" Alice laughed. In his address, the president said, "we will prevail!".
When should you not use an exclamation mark?
In exposition. Exclamation marks are reserved mainly for the quotations of people/characters. For some reason, when you, the author, begin using exclamation marks on your own words, it sounds and looks silly and contrived. That might be because the reader senses you're trying to force more emotion into your words than what is there.
As they ran, John suddenly slipped, as they fell over the cliff! Exposition. Don't do this.
There are very, very rare times when you can use an exclamation mark in exposition. There are no rules here, as it comes down entirely to author-feel. For now, just don't do it.
What should you do instead?
You mentioned you use exclamation marks to convey tone. Don't do that. Exclamation marks convey only one thing, and that is heightened emotion. They don't describe what that emotion is. (Fear? Love? Joy? Worry?)
Exclamation marks heighten an emotion you have already described. They themselves cannot describe an emotion in specific terms. Describe the tone. Show the tone. Have characters act based on the tone. But don't rely solely on exclamation marks.
Tears streamed down her face. "You promised!" she choked out. He threw his hat into the air. "The war is over!" he cried.
Note also that the verb can really help you. Instead of just saying 'said', get descriptive. Look back at my examples. You'll see that I used a word which was more descriptive than 'said' every time, and conveyed more emotion.
Multiple Exclamation Marks
You mentioned in comments on your question that you also wanted to know about too many exclamation marks at the end of a sentence. Generally, any more than one is left to the semi-professional writing at best. Adding multiple exclamation marks does not magically increase the emotional impact of what is being said, and runs the risk of making your writing look unprofessional. There is only one time I might use multiple exclamation marks:
"NO!!!!" "ANNA!!!" "RUN!!!"
One word. One moment of pure - whatever the word conveys - and nothing else. Even then, it is the all caps and not the exclamation marks which lend most of the volume and passion.
There is one other time you should consider multiple exclamation marks, and that is the dreaded '!?!' or '?!?'. These are rare, but they do occur in novels. My best advice is to see if the sentence works with either just a question mark or just an exclamation mark. Try using italics to emphasize a certain word or phrase, combined with just one of the end marks. If this works, use that. If not - and only then - use one of the above. I find that '!?!' suggests more of an exclamation while '?!?' is more of a question. Never go above three end marks. You can do two if you want, but I have found that they tend to look weird.
Best of luck in your writing! (See, there's an exception to what I just said.)