We employ the electronic spin of a single nitrogen-vacancy (NV) defect in diamond to detect and control the quantum state of remote nuclear spins coupled by hyperfine interaction. More precisely, our work focuses on individual 13C nuclei featuring a moderate hyperfine coupling strength (∼ 1 MHz) with the NV’s electron spin. Two different methods providing an efficient room-temperature polarization of these peculiar 13C nuclear spins are described. The first one is based on a polarization transfer from the NV electron spin to the 13C nucleus, which is mediated by the anisotropic component of the hyperfine interaction. The second one relies on coherent population trapping (CPT) within a Λ-type energy-level configuration in the microwave domain, which enables to initialize the 13C nuclear spin in any quantum state superposition on the Bloch sphere. This CPT protocol is performed in an unusual regime for which relaxation from the excited level of the Λ-scheme is externally triggered by optical pumping and separated in time from coherent microwave excitations. For these two polarization techniques, we investigate the impact of optical illumination on the nuclear spin polarization efficiency. This work adds new methods to the quantum toolbox used for coherent control of individual nuclear spins in diamond, which might find applications in quantum metrology.