The reconstructed and Na-adsorbed Si(100) surfaces are studied using a first-principles pseudopotential method. On the reconstruction of Si(100) surface, it is found that the buckled geometry of the asymmetric dimer leads to the reduction of the band energy, thus its energy is lower by 0.15 eV/dimer than that for the symmetric dimer. The higher order p($2\times2$) and c($4\times2$) reconstructions are energetically more favorable by 0.1 eV/dimer lower than the ($2\times1$) structure. These geometries show that the antiferromagnetic arrangement of dimers makes a gain in electrostatic energy through dipole-dipole interactions between dimers while the zig-zag buckling lowers the strain due to dimerization. However, between the p($2\times2$) and c($4\times2$) structures no appreciable energy difference exists. The band structures of the asymmetric dimers reveal semiconducting features with the indirect band gap energies of 0.1 eV for the ($2\times1$), 0.2 eV for the p($2\times2$), and 0.25 eV for the c($4\times2$) structures. For Na-adsorbed Si(100) surfaces, we choose the p($2\times2$) structure as substrate surface and investigate the preference of Na adsorption site, the character of bonding between Na and Si, and the saturation coverage. At the coverage of 0.5, the valley bridge site is found to be lowest in energy: 0.16 eV and 0.07 eV lower than the pedestal and cave sites, respectively. At the coverage of 1.0, the double layer model with the Na atoms at the valley bridge and pedestal sites is supported. The nature of Na-Si bond is found to be covalent rather than ionic. From the calculated formation energies, we suggest that the saturation coverage should be 1.0.