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Tidal effects have important imprints on gravitational waves (GWs) emitted during the final stage of the coalescence of binaries that involve neutron stars (NSs). Dynamical tides can be significant when NS oscillations become resonant with orbital motion; understanding this process is important for accurately modeling GW emission from these binaries, and for extracting NS information from GW data. In this paper, we carry out a systematic study on the tidal excitation of fundamental modes of spinning NSs in coalescencing binaries, focusing on the case when the NS spin is anti-aligned with the orbital angular momentum-where the tidal resonance is most likely to take place. We first expand NS oscillations into stellar eigen-modes, and then obtain a Hamiltonian that governs the tidally coupled orbit-mode evolution. We next find a new approximation that can lead to analytic expressions of tidal excitations to a high accuracy, and are valid in all regimes of the binary evolution: adiabatic, resonant, and post-resonance. Using the method of osculating orbits, we obtain semi-analytic approximations to the orbital evolution and GW emission; their agreements with numerical results give us confidence in on our understanding of the system's dynamics. In particular, we recover both the averaged post-resonance evolution, which differs from the pre-resonance point-particle orbit by shifts in orbital energy and angular momentum, as well as instantaneous perturbations driven by the tidal motion. Finally, we use the Fisher matrix technique to study the effect of dynamical tides on parameter estimation. We find that the dynamical tides may potentially provide an additional channel to study the physics of NSs. The method presented in this paper is generic and not restricted to f mode; it can also be applied to other types of tide.