Water (bath), wash cloth or https://en.wikipedia.org/wiki/Strigil
For thorough washing of clothes and other objects they were using lye, but lye would be too harsh for skin.
Perhaps they were first using earth to absorb most of the oil, which was then removed with the strigil, followed by washing with water.
Water (bath), wash cloth or https://en.wikipedia.org/wiki/Strigil