First important thing is asking them to show you or upload their voucher and the calculation summary (in Sacramento) to make sure they can afford the unit according to section 8 calculation, it called "rent affordability worksheet". In Sacramento, they have this posted on their website, you or tenant can put in the asking rent and the calculation will let you know if it is affordable. My experience here in Sac is people looking for the place but their voucher is not yet ready, I had to turn down handful of tenants that were not ready but wanted to rent my place.
Make sure to follow their inspection list, the inspector checked everything on that list, testing every single plug in my property, turn on every appliance, hot water.. very thorough.
Once you passed inspection, tenant can move in the same day. But process takes a little long before you get your first payment (about 3 weeks for me). Not bad here in Sac though since everything is online from turning tenant request called RFTA to rent negotiation through email, landlord portal, direct deposit set up. It makes things faster and easier online than paperwork like the old day.
Good luck!