Most comments make it seem so complicated.
If you go to HUD.gov you'll be mired in minutia. You can use HUD.gov to look up the Housing Authorities in your state. There may be overlap... such as there may be a Housing Authority for your county and another Housing Authority for a city in your county. They may or may not cover the same geographical area.
The Housing Authorities are local entities run by local government who administer the Federal HUD funds. They are separate and apart from HUD.gov but must abide by Fed HUD rules.
Your lease is with the tenant and eventually an agreement with the local Housing Authority as to how much they will pay toward the rent. The first year usually requires a one year lease.
You can just visit gosection8.com, which allows you to advertise to prospective tenants. You need to check prospective tenants vouchers (which are given to them by the Housing Authority) to see that they are allotted enough to cover the rent. (The Payment Standard) That allotment is based on # of bedrooms but in most cases, a person who has a one bedroom voucher can lease a 2, 3, 4 bedroom place as long as the rent doesn't go over the "Payment Standard" on that voucher.
Your prospective tenant fills out a simple form and sends it to the Housing Authority, which then schedule an inspection. The inspections are very fast, (maybe 10 minutes) unless your place is a mess. It's basic... screens in windows, hot water heater, bathroom and kitchen, etc. After the inspection approval, you go to the local HUD Housing Authority Office and sign the documents. You can also call your local HUD Housing Authority initially and tell them you're a landlord and would like to advertise your rental as your area may or may not use gosection8.com.
It's all very simple but it will take about 6 weeks for you to get your first rental check as they have to put you in the system. Then checks will arrive on time or even early.
The Housing Authority is strict on criminal background check regarding drugs or violence but you still want to run your own credit and perhaps criminal background checks. I don't know what one person referred to as a class for 3 days for landlord. Never heard of such a thing but maybe some local offices require it. Doesn't seem so as that would discourage landlords.