We present predictions for the fluorescent Lyα emission signature arising from photoionized, optically thick structures in smoothed particle hydrodynamic cosmological simulations of a ΛCDM universe using a Monte Carlo Lyα radiative transfer code. We calculate the expected Lyα image and two-dimensional spectra for gas exposed to a uniform ultraviolet ionizing background as well as gas exposed additionally to the photoionizing radiation from a local quasar, after correcting for the self-shielding of hydrogen. As a test of our numerical methods and for application to current observations, we examine simplified analytic structures that are uniformly or anisotropically illuminated. We compare these results with recent observations. We discuss future observing campaigns on large telescopes and realistic strategies for detecting fluorescence owing to the ambient metagalactic ionization and in regions close to bright quasars. While it will take hundreds of hours on the current generation of telescopes to detect fluorescence caused by the ultraviolet background alone, our calculations suggest that on the order of 10 sources of quasar-induced fluorescent Lyα emission should be detectable after a 10 hr exposure in a 10 arcmin2 field around a bright quasar. These observations will help probe the physical conditions in the densest regions of the intergalactic medium as well as the temporal light curves and isotropy of quasar radiation.