It has been shown that spectroscopy of transiting extrasolar planets can potentially provide a wealth of information about their atmospheres. Herein, we set up the inverse problem in spectroscopic retrieval. We use nonlinear optimal estimation to retrieve the atmospheric state (pioneered for Earth sounding by Rodgers). The formulation quantifies the degrees of freedom and information content of the spectrum with respect to geophysical parameters; herein, we focus specifically on temperature and composition. First, we apply the technique to synthetic near-infrared spectra and explore the influence of spectral signal-to-noise ratio and resolution (the two important parameters when designing a future instrument) on the information content of the data. As expected, we find that the number of retrievable parameters increases with increasing signal-to-noise ratio and resolution, although the gains quickly level off for large values. Second, we apply the methods to the previously studied dayside near-infrared emission spectrum of HD 189733b and compare the results of our retrieval with those obtained by others.