Epsom Salt does work great at naturally killing weeds and especially small weeds that are growing in things such as cracks, crevices and other small areas.
Larger weeds may take a bit longer to die off using Epsom Salt but it does work.
To kill weeds using Epsom Salt you mix the Epsom Salt with some vinegar and Dawn Dish Soap and then put it in a garden weed sprayer.
Then spray the mixture of Epsom Salt, Dawn Dish Soap and Vinegar onto the weeds and within 30 minutes you should see the weeds start to wilt and die off.
I use the Epsom Salt as weed killer which is cheaper and safer than the chemical based weed killer you buy commercially.