What is the best way to get rid of black mold?

The first thing to do is to find the cause of the moisture cause cleaning it with bleach and tilex won't fix the problem. Sure you can clean and scrub the mold away but unless you get the moisture problem fixed it's going to continue to be a problem and you need to get the mold identified to make sure it's not that kill you in your sleep type mold.

Are you keeping your house heated enough? sounds like condensation is allowing mold to grow. I have had that in the bathroom before. I changed from regular paint to bathroom paint and the problem was solved! it's a bit more expensive though. I continue to have this around the aluminium window frame because it's cold and humidity condenses there... and there are expensive products to kill and prevent the mold from coming back but it's indeed bleach (and this I checked with my microbiologist friend too). The only thing worth paying for is antifungal bathroom paint (use it in the affected rooms) and heating the room and ventilating the room sufficiently. If there was a source of damp coming through the walls from the other side, you would see more damage that's why I say it's from condensation. Oh you can always get a dehumidifier too.

You shoudl make sure you wear a mask because black mold is the deadliest

Tilex mold and mildew remover. Works wonders.

black mold should be removed by a professional not the average homeowner because it multiplies quickly

you are not getting any ventalation, air cirulation and fresh air... you are enclosed in not opening the windows enough... comet and water and a sponge that is all you need

bleach..