1. Colleges set exorbitantly high prices.
2. The government-supported system assesses families' ability to pay though FAFSA process, where you submit your tax returns (not that you have to, IRS is government as well) with your wage/business income, then list all your assets (minus retirement accounts such as 401Ks) and liabilities. Then the FAFSA spits out your expected contribution, TELLING you how much you can afford to pay for your kids education.
3. Colleges and government then use this number to determine how much "financial need" you have. They can "meet your financial need" by letting you pay less than the sticker price (it's called "need-based scholarship"), or allow to take loans on favorable terms to close the difference between the sticker price and your ability to pay (that they determined). More often it's a combination of the two (depending how desirable college is and how good of the student they perceive your kid to be).