I am asked this question by parents all the time, and yet, I find this a difficult question to answer. My answer is never definitive, but rather, a little more vague.
If I know the child really well, then I can answer with more specific information; however, I believe if a parent is asking this question, they are already on the path to providing a challenging environment for their child.
However, here are my top three things to do:
1. Follow your child's passion or interest and provide opportunities for further exploration: for example, one summer, my son was obsessed with tarantulas. So, I went to the library and signed out every book I could on tarantulas; we did some research on the web, and I took him to Science World where we visited the residential tarantula. From there, I learned of a bug museum where there was a variety of different tarantulas, so we went and visited a few times, and learned about the different varieties of these fascinating spiders. As well, we made a model of a tarantula and painted it; and my son drew pictures of the tarantulas. This was a great project for both of us and I learned a great deal about tarantulas. My son was five at the time, so this type of learning was appropriate for his needs; if he was older, perhaps I would have encouraged him to write about tarantulas, or create a story about tarantulas, or investigate why some tarantulas are considered endangered.
So find your child's interest and passion, and provide opportunities for your child to develop this area of interest, no matter what it may be!
2. Encourage reading, reading, reading and more reading: I can not encourage reading enough and I think it is the best way to challenge your child and have them learn about new things and have new perspectives on their world, and open themselves to new ideas. There are so many things to read besides books: newspapers, blogs, magazines, websites! For example, one of my sons loves lego, and he is constantly on the lego website, reading reviews of new items, meticulously reviewing the lego magazine, and watching reviews about products. He knows what items were released in what year, and what has been discontinued, and what are specialty items. He gleams all this information from reading!
So encourage and provide opportunities for reading by visiting your library or nearest bookstore, or search the web for fantastic teacher and librarian sites that recommend and review books.
3. Give your child free time to play and explore and they will discover who they are and what they are interested in: I firmly believe that a child needs time develop interests and passions. Get away from tv and computers and have your child play without results or outcomes. I call this tinkering....draw, write, build with lego, make a song, create a game, and go outside!
Giving your child time to play will help your child gain independence and will feed their passions.
Now, it may seem contrary to what you are expecting ( ie hours of skill and drill to make sure they master everything at grade level and beyond), but the bottom line is; follow your child's passion, provide help in getting them there, open up their world with literature and reading opportunities, and let your child work it all out through free time and exploration!