Take a fraction of the original solution and add it to a set amount of a neutral solution. For example, the original solution is red food coloring, and you extract 1 ml of the solution and add it to 9 ml of water.
Mix the extracted solution to the neutral solution to obtain equilibrium. For the example, mix the red food coloring with the water. Now you have obtained a 1/10 of the original solution and diluted the amount to the power of 10 to first degree or just 10.
Extract another fraction of the mixed solution and add it to another set amount of a neutral solution. For the example, extract 1 ml from the mixed solution and add it to another 9 ml of water. Mix the solution to obtain equilibrium. This will result in obtaining 1/100 of the original solution and diluted the amount to power of ten to the second degree or 100.