Thank you to Samual Yanz (N7FNV) for submitting a guide that he's created about tracking and decoding NOAA weather satellites. The guide can be downloaded from this link as a PDF.
Currently there are three operational polar orbiting NOAA weather satellites that transmit image data in the APT format at 137 MHz. When one of these satellites pass overhead, it is possible to use an RTL-SDR with appropriate satellite antenna and software to receive the satellite weather images they transmit.
Samual's guide focuses on the software and shows how to setup Virtual Audio Cable for piping audio between programs, SDR# for receiving the signal, Orbitron for tracking the satellite and WXtoIMG for decoding the image.