A variational approach is employed to compute the wave function of a single polaron for a two-dimensional Holstein Hamiltonian with arbitrary forms of linear particle-boson interactions and boson dispersion relations. The Toyozawa ansatz is utilized, and generalizations to multiple polarons are outlined. Applications are made to model superradiance in pseudoisocyanine bromide J-aggregates, and to calculate quasiparticle dispersion of an itinerant hole in a two-dimensional antiferromagnet.