There are multiple housing problems and they're all probably way more complicated than anyone wants to acknowledge. The highest priority "housing problem" right now imo is that there are people who don't have a safe place to sleep at night.

In order to solve that problem you need

1. Safe housing to provide to those people
2. A system for assigning those people to the housing.

Building/acquiring housing costs money. If the government isn't doing its job and spending money to solve this problem we need to

1. Hold them accountable through voting
2. Take matters into our own hands as a community and attempt to contribute to a local solution in whatever capacity we're able to contribute (donations, volunteering, organizing). Once we have legitimate trustworthy organizations that are doing a good job solving the problem then we can hopefully proceed by driving more support for them.

Creating a system to assign individuals to housing is probably the more "difficult" part because there needs to be some sort of consensus on the mechanics of prioritization. I personally think we should prioritize housing for individuals and families with children, but after that I don't know who we should serve next.