A dynamical coupled-channels formalism for processes $\ensuremath{\pi}N\ensuremath{\rightarrow}\mathit{KY}$ and $\ensuremath{\gamma}N\ensuremath{\rightarrow}\mathit{KY}$ is presented that provides a comprehensive investigation of recent data on the $\ensuremath{\gamma}p\ensuremath{\rightarrow}{K}^{+}\ensuremath{\Lambda}$ reaction. The nonresonant interactions within the subspace $\mathit{KY}\ensuremath{\bigoplus}\ensuremath{\pi}N$ are derived from effective Lagrangians, using a unitary transformation method. The calculations of photoproduction amplitudes are simplified by casting the coupled-channels equations into a form such that the empirical $\ensuremath{\gamma}N\ensuremath{\rightarrow}\ensuremath{\pi}N$ amplitudes are input and only the parameters associated with the $\mathit{KY}$ channel are determined by performing ${\ensuremath{\chi}}^{2}$ fits to all of the available data for ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{K}^{\ifmmode^\circ\else\textdegree\fi{}}\ensuremath{\Lambda},{K}^{\ifmmode^\circ\else\textdegree\fi{}}{\ensuremath{\Sigma}}^{\ifmmode^\circ\else\textdegree\fi{}}$, and $\ensuremath{\gamma}p\ensuremath{\rightarrow}{K}^{+}\ensuremath{\Lambda}$. Good agreement between our models and those data are obtained. In the fits to $\ensuremath{\pi}N\ensuremath{\rightarrow}\mathit{KY}$ channels, most of the parameters are constrained within $\ifmmode\pm\else\textpm\fi{}20%$ of the values given by the Particle Data Group and/or quark model predictions, whereas for $\ensuremath{\gamma}p\ensuremath{\rightarrow}{K}^{+}\ensuremath{\Lambda}$ parameters, ranges compatible with broken SU(6) \ensuremath{\bigotimes} O(3) symmetry are imposed. The main reaction mechanisms in ${K}^{+}\ensuremath{\Lambda}$ photoproduction are singled out and issues related to newly suggested resonances ${S}_{11},{P}_{13}$, and ${D}_{13}$ are studied. Results illustrating the importance of using a coupled-channels treatment are reported. Meson cloud effects on the $\ensuremath{\gamma}N\ensuremath{\rightarrow}{N}^{*}$ transitions are also discussed.