There are kids who have been admitted to MIT who were homeschooled through a combination of MOOCs, MIT OCW online classes, and presumably some standardization testing (SATs). Often, these kids are not from wealthy families (or could afford $30-40K for private school) and are homeschooling on a shoestring budget. I'm not sure how much standardized testing they do either. The good news is that it's entirely possible to gain entry into a prestigious school through homeschooling and not spending a fortune or going totally insane doing so.
Some MOOC classes you could pay for a certificate - $50+ to document for a transcript. Also, some MOOCs have tests and offer certificates for free or have test scores recorded for future documentation.
Lee Binz has a website and book on how to document things for college admission. Also, Cafi Cohen has a book, though it's a bit dated now. The key is to have a record keeping system and document everything. Some photocopy the table of contents in a textbook, for instance, for documentation and keep copies of some written work.
It's a good idea to check out websites on the colleges you're thinking about as places like MIT have web pages dedicated to homeschool applicants. You also could always ask someone on the finer details if necessary.
