With public schools, you can usually get a reasonably good idea of how much it will cost. If you are applying from out-of-state, there won't be much financial aid, except for loans, but there may be some scholarship money. You can often see a chart right on the school's website, with a grid showing potential scholarships for X GPA and Y SAT score. The key is to apply early, as the scholarship money often runs out.
But private schools? Private schools are different. Some have only need-based aid, but they are the ones who get to determine whether or not you have need. Others will offer a combination of need-based and merit based money.
How do you know which type of school will be a financial fit for your student? It takes a lot of research to figure it out. Schools do have calculators on their websites, but that will just give you a rough estimate of what it will cost.
Sometimes schools will sweeten the pot, for a student that they really want. They call this "Preferential Packaging". And sometimes they will use "Professional Judgement" to increase the aid for a particular family, based on their circumstances.
The bottom line (pun intended!) is that you need to do the research so your student applies to a good mix of schools, which will fit the family's financial parameters.
Read more about Paying for College