Local compositions and structures of Zn_{1-x}Mg_{x}O alloys have been investigated by Raman and solid-state {67}Zn/{25}Mg nuclear magnetic resonance (NMR) spectroscopies, and by neutron pair-distribution-function (PDF) analyses. The E2(low) and E2(high) Raman modes of Zn_{1-x}Mg_{x}O display Gaussian- and Lorentzian-type profiles, respectively. At higher Mg substitutions, both modes become broader, while their peak positions shift in opposite directions. The evolution of Raman spectra from Zn_{1-x}Mg_{x}O solid solutions are discussed in terms of lattice deformation associated with the distinct coordination preferences of Zn and Mg. Solid-state magic-angle-spinning (MAS) NMR studies suggest that the local electronic environments of {67}Zn in ZnO are only weakly modified by the 15% substitution of Mg for Zn. {25}Mg MAS spectra of Zn_{0.85}Mg_{0.15}O show an unusual upfield shift, demonstrating the prominent shielding ability of Zn in the nearby oxidic coordination sphere. Neutron PDF analyses of Zn_{0.875}Mg_{0.125}O using a 2x2x1 supercell corresponding to Zn_{7}MgO_{8} suggest that the mean local geometry of MgO_{4} fragments concurs with previous density functional theory (DFT)-based structural relaxations of hexagonal wurtzite MgO. MgO_{4} tetrahedra are markedly compressed along their c-axes and are smaller in volume than ZnO_{4} units by ~6%. Mg atoms in Zn_{1-x}Mg_{x}O have a shorter bond to the $c$-axial oxygen atom than to the three lateral oxygen atoms, which is distinct from the coordination of Zn. The precise structure, both local and average, of Zn_{0.875}Mg_{0.125}O obtained from time-of-flight total neutron scattering supports the view that Mg-substitution in ZnO results in increased total spontaneous polarization.
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