Tapered optical fibers with a nanofiber waist are versatile tools for interfacing light and matter. In this context, laser-cooled atoms trapped in the evanescent field surrounding the optical nanofiber are of particular interest: They exhibit both long ground-state coherence times and efficient coupling to fiber-guided fields. Here, we demonstrate electromagnetically induced transparency, slow light, and the storage of fiber-guided optical pulses in an ensemble of cold atoms trapped in a nanofiber-based optical lattice. We measure a slow-down of light pulses to group velocities of 50 m/s. Moreover, we store optical pulses at the single photon level and retrieve them on demand in the fiber after 2 microseconds with an overall efficiency of (3.0 +/- 0.4) %. Our results show that nanofiber-based interfaces for cold atoms have great potential for the realization of building blocks for future optical quantum information networks.