Heat the oil to 360 degrees F.
Remove the plantain slices with a slotted spoon and drain on paper towels.
When the plantain slices are cool enough to handle (about 1 minute), between paper towels, smash them into flat rounds using the bottom of a glass. Fry the rounds in the hot oil for another 3 minutes. They will turn crisp and golden brown.
Remove the tostones with a slotted spoon and drain on paper towels. Salt them as soon as they come out of the oil.