The screened Coulomb potential, or Yukawa potential, is used to illustrate the application of the single and linear variational methods. The trial variational functions are expressed in terms of Slater-type functions, for which the integrals needed to carry out the variational calculations are easily evaluated in closed form. The variational energies of the first two states of the screened Coulomb potential are calculated by minimizing them with respect to the exponential parameters included in the Slater functions using elementary minimization algorithms. The project allows students to concentrate on the fundamentals and the performance of the variational method at its increasingly accurate levels of application to realistic systems. (Contains 5 tables and 3 figures.)