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We study numerical methods for a mixed Stokes/Darcy model in porous media applications. The global model is composed of two different submodels in a fluid region and a porous media region, coupled through a set of interface conditions. The weak formulation of the coupled model is of a saddle point type. The mixed finite element discretization applied to the saddle point problem leads to a coupled, indefinite, and nonsymmetric linear system of algebraic equations. We apply the preconditioned GMRES method to solve the discrete system and are particularly interested in efficient and effective decoupled preconditioning techniques. Several decoupled preconditioners are proposed. Theoretical analysis and numerical experiments show the effectiveness and efficiency of the preconditioners. Effects of physical parameters on the convergence performance are also investigated.