The problem of perpendicular diffusion by a particle in a turbulent plasma is a problem of enduring interest and one that has yet to be fully solved. Analytic models do not agree with either observations or numerical simulations. Recently, a nonlinear guiding center theory (NLGC) was developed by Matthaeus et al. <2003> which, for the first time, appears to be consistent with numerical simulations in both the high-energy and low-energy particle regimes, provided that the transverse magnetic field is complex. Flux surfaces with high transverse complexity are characterized by the rapid separation of nearby magnetic field lines, and we show that the combination of slab and two-dimensional turbulence (a two-component model) is necessary to produce transverse complexity and that slab turbulence alone, for example, is insufficient. The nonlinear theory is expressed through the solution of an integral equation for the perpendicular diffusion coefficient $kappa$xx, which we solve approximately. Our approximate solution is in excellent agreement with the exact solution of the integral equation. The physical content of the NLGC theory is revealed clearly by the approximate solution and it is shown how $kappa$xx scales with parameters such as the energy density in magnetic fluctuations, mean field strength, particle gyroradius, MHD turbulence correlation length scales, parallel diffusion coefficient, etc. Unlike the integral equation formulation, which is not readily amenable to inclusion in models and numerical codes that require the perpendicular diffusion coefficient explicitly, the approximate model derived here is easily incorporated into, for example, heliospheric cosmic ray modulation models. Finally, the perpendicular diffusion coefficient is used to evaluate (1) the particle acceleration timescale for diffusive shock acceleration at perpendicular shocks and (2) the diffusion coefficient for cosmic ray modulation throughout the heliosphere.