Underwater acoustic (UWA) communication is an essential part of many civilian and military applications. For UWA sensor networks, the sensing information can only be interpreted meaningfully when the location of the sensor node is known. However, node localization is a challenging problem. Global Navigation Satellite Systems (GNSS), which are often used in terrestrial applications, do not work underwater. In this paper, we propose and investigate techniques for localization of a single-antenna UWA communication receiver with respect to one or more transmit antennas. These techniques are based on the matched field processing. Firstly, we demonstrate that a non-coherent ambiguity function (AF) allows significant improvement in the localization performance compared to the coherent AF previously used for this purpose, especially at high frequencies typically used in communication systems. Secondly, we propose a two-step (coarse-to-fine) localization technique. The second step provides refined spatial sampling of the AF in the vicinity of its maximum found on the coarse space grid covering an area of interest (in range and depth), computed at the first step. This technique allows high localization accuracy and reduction in complexity and memory storage, compared to the single step localization. Thirdly, we propose a joint refinement of the AF around several maxima to reduce outliers. For validation of the proposed techniques, we run numerical experiments in different UWA environments, with different parameters for the spatial sampling, number of transmit antennas and different accuracy for the estimation of the acoustic channel response.