This is surprisingly easy to do with some cheap hardware[0]. There is plenty of information if you just search something like "NOAA RTL-SDR." Building the antenna is the most labor intensive part, but still very easily done. I haven't personally, but it's on my to-do list for this summer.
[0] https://www.rtl-sdr.com/rtl-sdr-tutorial-receiving-noaa-weat...