"I want to be a member."
Translation:Üye olmak istiyorum.
That sounds like you're saying "I want to be one member." in Turkish. You don't need to use the indefinite article "a" in Turkish everywhere it's present in English.
Ok, that's a good way to translate it, I get it now :) Are there any specific rules when it's absolutely necessary to use it? Most of the time I haven't used it and it's been correct.
I don't know if there exists any steadfast rule of thumb on this, but those who support an economical or efficient use of words would tell you to omit a word if the meaning is clear without it. In other words, if the exclusion of the word doesn't make the meaning ambiguous, don't include it.
"Adamlar elma yer."
could mean "The men eat an apple," or "The men eat apples."
"Adamlar bir elma yer."
on the other hand, means "The men eat an apple."
That really doesn't apply to this sentence. Nevertheless, in English we would never say, "I want to become member (general meaning)," or "I want to become members." Basically, in this sentence, little room, if any, exists for ambiguity, so why add "bir" to it?
Bottom line? Word for word translations may not always convey the same meaning. Sometimes adding "bir" will clear up ambiguity and other times it will convey something you don't mean. The best thing you can do is learn why you got something wrong. Sometimes you'll be able to apply it to other situations and sometimes you won't.
Hoped that helped in some way.