Increase taxes on rental income on single-family homes and double the property tax on vacant homes to discourage hoarding.

Encourage building upwards to increase housing supply. This can be done via tax breaks or subsidies. Especially encourage multi-use buildings to make cities walkable. Stores/restaurants at the street level with apartments above.

Ditch or reform/restrict the 30-year fixed-rate mortgage. Remove barriers to building more housing. Other stuff, but you can do a web search, I'm sure.