Mix the salt with dish soap or vinegar (tap water can also work). Using a moist rag, work some Epsom salt over your grout. Let it sit overnight, and wipe clean in the morning.
Try mixing Epsom salt with an equal amount of dish soap for a quicker option. Rub it onto your grout and let it sit for as long as possible, but not overnight.
If unsure how a surface will react, test in a small area to see if the Epsom salt and dish-washing liquid will scratch, discolor, or otherwise warp the tile and grout.