We characterize a novel fluorescence microscope which combines the high spatial discrimination of a total internal reflection epi-fluorescence (epi-TIRF) microscope with that of stimulated emission depletion (STED) nanoscopy. This combination of high axial confinement and dynamic-active lateral spatial discrimination of the detected fluorescence emission promises imaging and spectroscopy of the structure and function of cell membranes at the macro-molecular scale. Following a full theoretical description of the sampling volume and the recording of images of fluorescent beads, we exemplify the performance and limitations of the TIRF-STED nanoscope with particular attention to the polarization state of the laser excitation light. We demonstrate fluorescence correlation spectroscopy (FCS) with the TIRF-STED nanoscope by observing the diffusion of dye molecules in aqueous solutions and of fluorescent lipid analogs in supported lipid bilayers in the presence of background signal. The nanoscope reduced the out-of-focus background signal. A lateral resolution down to 40-50 nm was attained which was ultimately limited by the low lateral signal-to-background ratio inherent to the confocal epi-TIRF scheme. Together with the estimated axial confinement of about 55 nm, our TIRF-STED nanoscope achieved an almost isotropic and less than 1 attoliter small all-optically induced measurement volume.