Dancers start at all ages. Those crazy awesome kids you see on Dance Moms start the minute they can walk, or even before. My favorite contemporary teacher started in college (and ended up majoring in it too). I started at age 5, but didn't start taking more than 1-2 hours a week until age 15 (and am now majoring in it in college). SYTYCD and internationally famous choreographer Sonya Tayeh (lover her.) started seriously dancing at age 17. It is literally never too late or too early to start. But I'm getting off topic.
Many young girls (and some young boys!) start dancing at a young age, most of them as an after school activity, to meet friends, or just for fun. Some start (like on Dance Moms) training for their Broadway career at age 3, which is okay too. There's many different approaches, but most of them start with a ballet or tap class at a studio.
Let me say this first: I believe that, no matter what style you (or your child) intend(s) to pursue in the future, ballet is a must. Don't believe me? Olivia "Chachi" Gonzales of I.aM.mE crew is ballet/modern/jazz/lyrical trained. My college jazz teacher told me to take another ballet class because my technique and strength was a little weak. Surprised? Don't be. Ballet is the basis of all movement just as the alphabet is the basis of the English language. Professional football players take ballet. Martial artists take ballet. All dancers need it for the strength, discipline, and body alignment that ballet delivers.
This is my opinion on the ages which young dancers should start each style of dance (not including folk dances, ballroom, classical country-specific dances, and other specialty types. Please note that the styles indicated with an * should be continued past the age I have indicated to ensure a well-rounded foundation for college and/or professional careers. These are the bare minimum!):
- ballet*: ages 3-9
- tap: ages 3 and up (I've never taken a tap class in my life though. Oops.)
- jazz*: ages 8-12
- modern*: ages 9-15 (please do not confuse Modern with Contemporary. By Modern, I am referring to written techniques, like Graham, Horton, and Limon. Many studios do not offer such styles.)
- lyrical and contemporary: ages 10 and up
- hip hop and street styles: ages 10 and up
- pointe: ages 10-15 (also depends on when the teacher feels the student is ready, whether or not the child's feet are strong enough to handle the training, and the number of years and level of ballet training achieved. Never start pointe on your own.)
All in all, there are many approaches. Serious competition studios train young dancers that are more technically accomplished than I am at college age. Other studios, such as the studio I attend, are "family" studios that train for fun. Still others prepare dancers for professional careers without beating down on the children and depriving them of childhood. Look for a studio that fits your needs, but remember that when dance starts becoming work and suffering instead of fun and freedom, it may be time to lighten up or find a different passion.