The static and dynamic properties of ${\text{V}}^{4+}$ spins $(S=1/2)$ in the frustrated square-lattice compound ${\text{Pb}}_{2}(\text{VO}){({\text{PO}}_{4})}_{2}$ were investigated by means of magnetic susceptibility $\ensuremath{\chi}$ and $^{31}\text{P}$ nuclear magnetic resonance (NMR) shift $(K)$ and $^{31}\text{P}$ nuclear spin-lattice relaxation rate $1/{T}_{1}$ measurements on a single crystal. This compound exhibits long-range antiferromagnetic order below ${T}_{\text{N}}\ensuremath{\simeq}3.65\text{ }\text{K}$. NMR spectra above ${T}_{\text{N}}$ show two distinct lines corresponding to two inequivalent P sites present in the crystal structure. The observed asymmetry in hyperfine coupling constant for the in-plane (P1) P site directly points toward a distortion in the square lattice at the microscopic level, consistent with the monoclinic crystal structure. The nearest- and next-nearest-neighbor exchange couplings were estimated by fitting $K$ versus temperature $T$ by a high-temperature series expansion for the spin susceptibility of the frustrated square lattice to be ${J}_{1}/{k}_{\text{B}}=(\ensuremath{-}5.4\ifmmode\pm\else\textpm\fi{}0.5)\text{ }\text{K}$ (ferromagnetic) and ${J}_{2}/{k}_{\text{B}}=(9.3\ifmmode\pm\else\textpm\fi{}0.6)\text{ }\text{K}$ (antiferromagnetic), respectively. $1/({T}_{1}T\ensuremath{\chi})$ is almost $T$ independent at high temperatures due to random fluctuation of spin moments. Below 20 K, the compound shows an enhancement of $1/({T}_{1}T\ensuremath{\chi})$ which arises from a growth of antiferromagnetic spin correlations above ${T}_{\text{N}}$. Below ${T}_{\text{N}}$ and for the field applied along the $c$ axis, the NMR spectrum for the P1 site splits into two satellites and the spacing between them increases monotonically with decreasing $T$ which is a direct evidence of a columnar antiferromagnetic ordering with spins lying in the $ab$ plane. This type of magnetic ordering is consistent with expectation from the ${J}_{2}/{J}_{1}\ensuremath{\simeq}\ensuremath{-}1.72$ ratio. The critical exponent $\ensuremath{\beta}=0.25\ifmmode\pm\else\textpm\fi{}0.02$ estimated from the temperature dependence of the sublattice magnetization as measured by $^{31}\text{P}$ NMR at 11.13 MHz is close to the value (0.231) predicted for the two-dimensional XY model.