If you've got a brilliant kid, you'll already be well aware of what a fantastic, magical experience it is. Some kids have been known to take apart and put back together cell phones- At age two. Some are very quiet, and will play peacefully until you notice they've created something dazzling. Getting your mind blown on an hourly basis is the usual result. Even toys can become a sort of "bassinet university".
The brilliant kids need Mom and Dad as sounding boards, as much as parents. These kids are very highly focused, and they're limited by what they can access, as kids. You need to show them how to explore their areas of interest. You also need to make sure they can develop their skills naturally, without them getting derailed by too many external factors.
The fact is that talent and intelligence grow better on their own terms. Without the slightest need to push, a child can become an expert on any subject where their intellects are really engaged. You'll find you learn a lot. Talented people, of any age, are excellent teachers, and if you didn't know something about how to build a super computer or raise a giraffe, you'll find your six year old can explain it very clearly.
The needs of a brilliant child
What a really brilliant kid needs is information, and to be able to check their thinking properly. This is important, for skills development.
As a parent, you can contribute a lot, and you'll have a ball doing it:
Ask questions: Not "parent" questions, but adult questions. The child will react to any good question very well. Don't be too surprised if you get a better answer than you'd have given yourself.
For example, about a really great picture:
Don't ask: "Did you pick the colors yourself?", which is insulting, and proves you've missed the whole point of the picture. Ask an adult question instead "How did you decide which colors/what materials to use?"
The idea is that the kid examines their own thinking. You'll get a good answer, too, and you can expect some interesting ideas.
When you know a brilliant kid is interested in something: Give them exposure to new things in that area, things they haven't seen before. This stimulates further development, saves time for the kid in finding these things for themselves, and allows them to make the associations between simple and advanced things in their areas of interest early. Check out online toys in that field, too, some are excellent.
Access to information: The truly brilliant kids pick things up with incredible speed. If you help them to learn to read and how to get information, and make sure they have the basics, they'll do the rest to a very large extent.
The shy brilliant kid: This type of child isn't some sort of sociopath. They're wary, probably with good reason, of the "kiddies" environment. It's too dumb for them. They can't really associate with these people on any meaningful level, and wouldn't, if they had a choice. Leaving them stuck in "dumb land" is what makes them antisocial later, and who could blame them?
Have fun, and enjoy every second.