To minimize the amount of aluminum needed to make a soup can with a volume of 2.5 liters, the document provides steps to: 1) recognize the can is a cylinder, 2) write the equations for volume of a cylinder and solve for height in terms of radius, 3) take the derivative of volume and set it equal to zero to find the radius that minimizes surface area, and 4) use the minimizing radius to calculate the dimensions and minimum surface area required.