Many ballet summer intensives require auditions. Some will accept a DVD or VHS tape of you dancing, and they will specify what they want to see, to determine the level and accuracy of your ballet technique and ballet positions. If you search on the internet for summer intensives, there are pages and pages of results to view.
Some schools tour with audition classes. Another outreach is, for example, The Princeton University summer intensive can be auditioned forin Toronto, Canada, at the National Ballet School.
Look for details on every web site. Some summer intensives offer housing in dorms or "host family" homes. Many do not offer any housing. Parents, I'm sure, are concerned about the kind of environment where the summer intensive they choose is located.
Many parents and ballet students want an out-in-nature environment where a school may offer more than ballet classes.
And many serious ballet students know that, in order to be able to audition for the college dance department of their choice later, they need to focus on ballet and other dance styles now, to the exclusion of all else.
Spending a couple of summers away from home can be helpful for ballet students. Some may discover that they do not agree with the ballet lifestyle after all, even though they love dancing. The intensity, the competition, the sub-culture aspect of dance, is not a life that is meant for everyone.
If this is true for you, or if your real talent will come out best in some other performance venue such as acting, modern dance, singing, or in another field entirely, the sooner you discover this, the better.
There are many ballet summer intensives to choose from. Some will require auditions, and at the least, DVD or VHS auditions. Be prepared to pay an audition fee, and bring a photo of you dancing, and perhaps a head shot, to leave at the audition, if requested. Audition nerves can be a challenge, but you can train your brain out of those if you know how to.
Also bear in mind that smaller more local schools may offer better classes, even though they do not bear a famous ballet school name or have famous guest faculty. Depending on your age and level of training, it may be better to stay close to home, and continue to benefit from smaller classes and the familiarity that has nurtured you so far. You will know when you are ready for a bigger and strange environment. Even if you feel the audition nerves, you will want to go for a bigger challenge.
If you feel like the audition nerves are going to be overwhelming, take a look at "Train Your Brain" by dance medicine specialist Deborah Vogel. It is not written just for ballet dancers, but for all young people, to help understand how you can replace negative thoughts with positive emotions, and from there, better any situation that you choose to change.
Whatever summer ballet intensive you find, once you are accepted and registered, you have a grand adventure to look forward to!