what are some of the solutions to the lack of affordable housing?

The author of Evicted, Matthew Desmond, offers some practical solutions to the housing crisis. His main proposal is for the introduction of vouchers as a means of institutionalizing affordable housing. The principle on which this proposal is based is the same as that of food stamps. Just as food stamps allow poor families to buy groceries virtually anywhere, housing vouchers would enable families below a certain income level to obtain housing in many locations.
Effectively, this would be a federal subsidy designed to ensure that the poor would have somewhere to live, while at the same time allowing landlords to continue to make money from their property investments. Desmond's voucher proposal represents a radical departure for those advocating government involvement in housing. Instead of federal funds being used to build housing projects, they're to be put directly into the pockets of prospective tenants to give them some degree of choice as to how and where they'll spend their vouchers.