Before I try to answer this question (and probably make things worse), let me explain how I come up with my answers. I believe in native-speaker intuition. If the little voice in your head is saying "that sounds right", then it's probably right. However, if that little voice is saying "that sounds weird", it probably is. The more you test your little voice with standard reference books, the more confident you will become in trusting your intuition. (I call my little voice "Tater" because my wife wouldn't let me name our son "Tater". Let's face it, the potato is the wonder food. We need to celebrate it.)
But I digress. One of the reasons I left academia (I was a tenured professor at a university in Japan for four years) is because I got tired of having to defend every little utterance against "Where's your data?" "Show me your research?" "What does the literature say?" Take a pill. I believe common sense and experience are equally valid tools in the decision-making process. (It's also much easier and I'll never be accused of being a workaholic.) My point is - trust your gut. I trust mine. And I have more to trust than most these days.
I'll be the first to admit I've had it easy, following this gut-led charge on grammar, because I teach non-native speakers in a high school ESL program. Basically, I can tell them whatever I want and they have to believe me. "Go ahead. Prove that I'm wrong." And if they do, I ruin their chances at Harvard with a C-. (I'm kidding of course......or am I?) I guess what I'm saying is: listen to me at your own risk. You're not going to see a lot of works cited.
Back to the issue at hand, bring or take?
The simplest answer I can give is to use them like you use come and go. Imagine you are talking to a friend during lunch in the school cafeteria. When you are talking about moving away from your current location, you say "I'm going to the mall after school." If you are talking about moving towards your current location, you say "I came to school extra early this morning." Similarly, you would take your books with you to the mall and you would bring your computer with you to school. When you go somewhere, you take stuff with you. When you come to a place, you bring stuff with you.
However, it can get trickier. Imagine you will be attending a potluck supper after church on Sunday. (Man, I miss those.) On Friday, you talk with your friend Susan, who attends the same church.
You: Are you going to the potluck on Sunday?
Susan: Yes. I'm going to take my favorite tuna casserole.
You: We're going to take an apple cobbler.
On Sunday, both of you will be moving away from your homes so you go to church and take the dish when you leave the house.
Then later in the day, you bump into the minister.
Minister: Are you coming to the potluck after church on Sunday?
You: Yes. We're looking forward to it. We're bringing an apple cobbler and Susan is bringing her tuna casserole.
In this case, even though neither of you are at the church, you are talking about the minister's "home" and you will be moving towards that "home" on Sunday. Therefore, come and bring are appropriate.
To summarize: Remember the pairs: come/bring and go /take. Before deciding whether to use bring or take, ask yourself whether come or go would be appropriate. Then use its partner. However, before doing this, remember that I haven't eaten breakfast yet, so my gut might be grumpy and deliberately leading you in the wrong direction.