For parents out there: how do you know your child is good at something or excels in a hobby/subject? Do you sign them up for various classes and hopefully they'll excel in it?
Do you train them at home to be good in something YOU want them to be good at? (Math, spelling for spelling bee).
When you find out your kid is good at something do you exploit it/take advantage? (ie, try to get them a scholarship based on that or enter them in competition?)
Raising three kids, we never tried to train/steer them toward any particular interest. It always came from them. If THEY showed an interest or appitude for something, then we'd help them take things to the next level (materials, classes, etc.) IF that's what they wanted.
This isn't to say that they weren't exposed to various activities. We just didn't push them in any particular direction. None of our three kids showed any interest in sports, but all three excel in the arts. Our oldest is very good at drawing and writing (many people have told him he should be writing for SNL or stand-up comedy

) but he has chosen to work in the field of computer science.
Our middle child graduated summa cum laude with a BA in theatre and secondary education. From the time she was two years old, she showed an interest in singing and acting. All throughout her school years, she was heavily involved in choirs, drama programs, community theatre, basically anything that put her on a stage.

She was very good, but she worked very, very hard at everything she did. She was very motivated and determined to go after whatever it was she wanted. She also excelled academically, and was rewarded with a nice scholarship package for all four years of college (which she ended up finishing in three years). She is now teaching music/drama part-time at the high school level.
Both of our older kids definitely showed an interest, and have skills and talent, in a particular area. It was our youngest, however, that took "being good at something" to the next level.
Our younger daughter did a lot of community theatre starting at the age of eight. She mainly did it because she wanted to do whatever her older sister did. Turns out, she had a natural talent for acting. It came very easy to her and she was very good. We know she was good at it because she was offered leading roles in almost every show she auditioned for. At the age of 10, she played Helen Keller in The Miracle Worker. Her performance was incredible. Around the age of eleven, she decided she didn't want to do any more theatre.
When she was thirteen, she decided to take a hip-hop class because several of her friends were taking it. Up until that point, she had never shown any interest in dance. The class was one hour a week from September to June. At the end of the year, the studio director approached our daughter and asked if she'd be interested in auditioning for the studio's hip-hop competition team. She did, and she earned a spot on the team. Things just took off from there.
It was quickly apparent that our daughter had a raw, natural talent for dance. She started taking five and six dance classes a year, and was on as many as four or five different competition teams each year. She quickly caught up to (and surpassed) the skills of girls on the teams that had been dancing for ten or more years. Our daughter started performing solo routines at competitions and earned many first place/top awards. She was told over and over again, by dance teachers, directors, choreographers, competition judges, etc., how good she was, and that she just had that certain something, the "x" factor, raw talent, whatever you want to call it. Funny thing was, our daughter didn't always see it or believe it. She didn't have the self-confidence that many other girls had. There were many instances where she ended up winning first place in a competition, beating out hundreds of other dancers, and SHE would be the most surprised by the results!
To make a long story short (I know, not possible now!) I don't think a child should be pushed in a particular direction. I think it needs to come from the child. I think if a child is really good at something, it'll somehow come out.
As far as our younger daughter, she is now a sophomore in college, but is not majoring in dance. However, dance continues to be a big part of her life. She has been in several dance companies over the years, has trained with and danced for an LA choreographer, and continues to attend dance workshops.
The best part, she also teaches 8 to 10 classes a week at several local dance studios, and does choreography for competition/dance teams. At $20./$25. an hour (and $25. for the 1/2 hour private lessons she teaches) she is earning good money while she attends college. She knows how lucky she is to be making money for something she is good at and loves to do.
ETA: I do think kids can be good at things and also be trained to be good at things. But I do think many times, it is evident if a child has a natural talent or appitude for something. A person can train and take professional lessons in acting, for example, but someone that just has that natural ability will shine even without the lessons. Of course, if someone is really good at a particular skill AND has that raw talent, lessons will take them that much further. I hope all that makes sense!