We present a self-contained description of the wave-function matching (WFM) method to calculate electronic quantum transport properties of nanostructures using the Landauer-Büttiker approach. The method is based on a partition of the system between a central region ("conductor") containing $N_S$ sites and an asymptotic region ("leads") characterized by $N_P$ open channels. The two subsystems are linearly coupled and solved simultaneously using an efficient sparse linear solver. Invoking the sparsity of the Hamiltonian matrix representation of the central region, we show that the number of operations required by the WFM method in conductance calculations scales with $\sim N_S\times N_P$ for large $N_S$.

22 pages, 8 figures