Okay . . . strictly speaking:
"Because" is used to set up a reason for the clause it modifies:
Because I was speeding, I got a ticket. ("Because I was speeding" modifies the main clause "I got a ticket." It basically tells why.)
I got a ticket because I was speeding.
Because I ate so much cake, I got sick.
I got sick because I ate so much cake. (again, "Because I ate so much cake" modifies the main clause "I got sick.")
Note "because" can be used either in the begining or the middle of a sentence.
If you're answering a question, e.g. "Why were you late?" It's acceptable to simply answer "Because I got a ticket." because the subject/main clause of the sentence is implied. It would be very redundant to restate the question, and you'd probably irritate the person you were talking to if that's how you always responded. In very formal writing, however, this would be incorrect.
Colloquially, "since" can be used interchangably with "because."
Formally (correctly,) "since" is only used to refer to temporal (time) relationships. Thus, the only correct way to use "since" is the following:
I've had a bad back since I was a child.
Since watching that movie, I've been afraid of ham sandwiches.
"for" and "as" are a little bit more difficult for me to explain, because they're not typically used to show causation. If you could post a rough example of a sentence using for/as for causation, I could probably help you more.
For now, "as" and "for" are just prepositions. The only outstandingly special thing I can think of is that "as" can be used to set up a metaphor. Other than that, they're used like the other prepositions.
Colloquially:
Any one of those words you've mentioned can be used to say "because," although "as" and "for" aren't used very frequently. It's not necessarily correct, but native English speakers do it constantly. If you're speaking colloquially, there really aren't any rules as to which word is used when and for what purpose. That's the "thing" about colloquial speech.