It's been my experience that comma use is almost always a subtle affair. At times, a comma that at other times would be utterly necessary is dispensable.
The purpose of commas is to make clear the meaning of a sentence. If a comma only obfuscates the meaning, it should be discarded.
There are two helpful guides (but they should be used with reason):
1. Read it aloud. Commas should be placed where in normal speech a pause exists.
2. Take a step back, look at the comma, and if the comma looks ill-placed or unnecessary, drop it.
The most common use of the comma is for the joining of two independent clauses that are linked by a conjunction.
Commas also appear to separate appositive clauses and adverbial (and sometimes prepositional) clauses at the beginning of the sentence.
The main rubric for comma-use is: does the clause that's separated out by the comma refer to the surrounding clauses restrictively or non-restrictively. Meaning that if the clause weren't in the sentence at all, would the other clauses make sense or not?
i.e. I had gone to the place where I once lived, to reclaim my past.
I had gone home, where I have lived for the past 15 years.
In the first sentence, the only way you could excise the 'where' clause is if the place being spoken of were implied by previous sentences. Otherwise, since the 'where' clause is necessary for the meaning of the preceding clause, it should not be separated from it by a comma. The first two clauses are complete together and would not be meaningless if the last clause were left off. Therefore, this last clause is nonrestrictive and needs to be separated by a comma.
In the second sentence, the first clause is complete in meaning. The adverbial clause only adds further definition.
Of course, there are other rules, some of them very weird. For example, normally you would not put a comma before 'but' unless it were conjoining two independent clauses:
i.e. I have tried to explain myself, but I'm not sure I'm being clear.
I have explained myself but without clarity.
This second sentence, however, could bear a comma before 'but.' This is because the two clauses introduce a tone of opposition. Similarly, we would write, 'I am typing now, not surfing.'
Strunk recommends always including a comma before but, but I think that would disrupt the flow of many sentences. So, I try to be careful with 'but' commas.
Another odd rule is that when 'so,' 'thus,' 'then,' etc. begins a sentence, there should be a comma after it. Sometimes this is the case, sometimes not.
i.e. So, if you want me to buy you some chips, you're going to have to give me some money.
So he ran down to get me chips.
In the first sentence, 'so' is more of a colloquial delay-word. In the second, it's more adverbial in tone.
Then, could you remind me tomorrow, because I may forget.
Then he reminded me, because I had forgotten.
Also remember that a comma should always be used to separate conditionals.
Anyway, there are many other nuances, but the rule of restrictive and non-restrictive clauses is most critical for the understanding of comma-use.
Happy practicing.