How do you protect a brilliant idea when founding a startup?

Yeah, you're probably being a bit paranoid. Even if you think the idea is amazing, most people are working on their own amazing ideas and are emotionally tied to them rather than your's. Or they're just too lazy or busy to steal it anyway.
But sure, some caution is fine. I believe in talking to as many people as possible, but one on one with people you have relationships with, even if it's just that you clicked with them at a networking event. I would also avoid sharing it with near-direct competitors or posting it on Hacker News or something like that.

As mentioned in your question that should we keep it for ourselves or should we talk (share) with others (or even when you start up and people grab it), kindly see below my suggestion for your reference:

1. If you do not need to share as you know very well, while being afraid of others to take it. Then you can have it registered at the Department of Intellectual and Property Right. If it's not under categories that under protection list of this Department, then the only way is to have it implemented as soon as possible. Have you heard of entry barriers? leading will be your advantage and followers will need time to catch your position (in fact, it may not be this way, to some extent. Further discussion will follow if you are interested)

2. If you are unsure and it requires you to discuss with others. This means you need to obtain contribution, suggestion and or expertise from a sub set of people to redefine your idea, then you should know the people who you can trust and, of cause have appropriate knowledge on that issue.

Now a days, keeping an idea is not a common way for business success. It, in stead, requires a lot of contribution from people as we never can see through one thing in full in one moment, that's why we need team work. Take a simple example that you never can see everything in a football match (you follow the ball and not have view what's the goal keeper does at that moment), but different viewers will catch the things that you don't, and vice versa. One more thing that we are in functional society now, not self supply as age stone. So definitely we need a team or associates/ partners. Who are they? are they trustworthy? This is also an important element when you initiate a brilliant business concept. Why don't you study the model of multi national companies? they own business secrets while no one can steal. Or small/ household business models, they have their secret maintained through generations.

Cheers,

You are making mistake if you are not sharing this idea for others before you start. People usually thing that their idea is brilliant and causing of natural selfish especially Vietnamese we are, you will not discussing the key factors within your brilliant idea...
Don't forget to Google it before you think it's unique.

Thank you all of you for your precious sharings. After studying all the answers, I can infer nearly the same point is that for start-ups in today's market, it is not easy to survive by keeping the idea for our own. In doing business, nobody can ever succeed all alone and (more than) two heads seems to be much better than one:)
The point is to share the idea with the RIGHT people, at the RIGHT time!

More expertise, more experience, more knowledge accumulated can nurture the business idea to be more and more potential, feasible and profitable, right? However, showing everything you have is not a clever choice. I really like the advice of Mr. Csaba: "Talk about WHAT can you solve, and keep for yourself HOW". The key of every business idea lies in the HOW and only the idea owner can know what it's like :)

I have recently seen many people share their ideas with Anphabers and got very helpful advices. Now, I get to understand why Anphabe chooses the motto: Success shared is success multiplied:)

I think we should ask people around for our ideas. We might find something useful to implement our ideas well or just to stop it (if it is unrealistic :-)). From an idea to a realistic result is time consuming. Talking to other about our ideas is one of first steps to test its applicableness.