The theory of static and dynamic scattering of neutrons and light on microemulsion droplets is developed. The droplets are modeled by double-layered fluid spheres immersed in another fluid. The surface layer of arbitrary thickness thermally fluctuates in the shape. The scattering functions are consistently calculated up to the second order of the fluctuations. The bulk fluids and the layer are characterized by different scattering length densities (or dielectric constants). Involving the Helfrich's concept of interfacial elasticity, the theory is applied for the description of small-angle neutron scattering (SANS), neutron spin echo (NSE), and dynamic light scattering (DLS) experiments on dilute microemulsions. From the fits to the experimental data the bending elasticity and the Gaussian modulus are extracted. Due to the corrected account for the fluctuations, their values differ markedly from those obtained in the original works. The theory well describes the SANS experiments. In the case of DLS, we had to assume the shell of the solvent molecules to be built of several layers. Previous theories were in a sharp disagreement with the NSE experiments. A better agreement with these experiments is obtained if the dissipation in the surface layer is included into the consideration. From the experiments, the viscosity of the layer is estimated for a concrete microemulsion system.