Killing mold depends on the type of mold, and different molds require different things to kill them, which also depends on the type of surface they are on.

Chemicals

There are a variety of commercial and retail mold removal products around, and there's just as much variety in how effective they are. Just doing an online search, here's a page that has a variety of options of chemical sprays.

Best Overall: RMR-86 Instant Mold & Mildew Stain Remover at Amazon
"It works on nearly any surface and promises to remove stains in 15 seconds."

Best for Shower: Skylarlife Mold & Mildew Gel Stain Remover at Amazon
"It’s a gel so it doesn’t run down the walls like liquid versions."

Best for Bathroom: Tilex Mold and Mildew Remover Spray at Amazon
"Kills mold and other bacteria like staph, strep, and even fungus."

Best for Fabric: Micro Balance EC3 Laundry Additive at Amazon
"An all-natural product that you add to your regular laundry detergent."

Best for Wood: Concrobium Mold Control Household Cleaners at Amazon
"Works on boats, decks, attics, and more."

Best for Concrete: Wet and Forget Moss Mold Mildew Remover at Amazon
"Use the formula to wet the affected area and then forget it."

Best Natural: CleanSmart Daily Surface Cleaner at Amazon
"Non-toxic option for use on a daily basis."

https://www.thespruce.com/best-mold-removers-4583978

Natural options

I've found that hydrogen peroxide (H2O2) works really well on a variety of molds, including black mold. It has a chemical reaction that can't be avoided with the mold cells, similar to how it reacts when cleaning out a cut. It bubbles, releasing oxygen (O2) and water, which means there's really no cleanup, except for removing the debris of the mold itself.

Using too much bleach on a mold can actually cause it to go into a type of hibernation mode that makes it look like it's dead, but isn't. It'll eventually come back as if it never left. And getting the right amount of bleach on mold is generally a secret that keeps mold removal companies in business.

There are other non-hazardous chemicals that can be used to remove mold, with a variation on how well they work and what types of mold they work best on. These are inexpensive and easily acquired, since you might already have them.

1. Hydrogen Peroxide
2. Vinegar
3. Baking soda

https://www.maids.com/cleaning-hacks/3-non-toxic-ways-clean-mold-natural-cleaners/

Another list

Here's another list of mold killing options. Some are duplicates and it varies between harsh chemicals and natural removers.

Bleach
Borax
Vinegar
Ammonia
Hydrogen peroxide
Detergent
Baking soda
Tea tree oil
Grapefruit seed extract

https://moldpedia.com/mold-removal

Identification

The first thing to removing mold is to figure out what type it is, as best as possible, and then do an online search from there. There's likely a lot of information about how exactly to remove it, which will likely include one or multiple of the products listed above to kill it.

This site seems to cover a good number of common molds, but it's by far a comprehensive list. It includes descriptions of what the mold is and does, and even has pics to show exactly what it looks like. Beware: if you're squeamish, this might not be such a fun read for you, but there's nothing too horrible about it.

https://www.wideopencountry.com/the-12-types-of-mold-how-to-recognize-the-most-common-types-in-your-home/