The Dirac-Frenkel/McLachlan variational principle (DFMVP) is re-derived using a general and strict formalism which is valid for ail practical applications. General equations of motion for the parameters are derived from the DFMVP. The time-dependent parameter set solving the equations of motion forms an approximate variational solution of the original problem. An error estimate for the approximation is presented which shows that the variational solution converges to the exact one if the parametrisation is improved.