From where do weather radar maps get their data?
Images showing clouds mostly come from geostationary satellites. Geostationary satellites are at an altitude of about 36000 km, which allows them to monitor the same area of the Earth continuously. They stay in place relative to the Earth's surface above the equator thanks to balance between gravitational and centrifugal force. There are a few such satellites designated to operational weather forecasting, notably:


GOES-East &amp; GOES-West operated by NOAA
Meteosat-7,-8,-9,-10 operated by EUMETSAT
MTSAT operated by JMA (Japan)


These satellites contain passive remote sensing instruments measuring incoming radiation in a number of channels, mostly visible and infrared. Visible is only available during the day, while infrared is available all the time. Radiation is captured on lines of sensors by scanning the view, which generally takes a few minutes to complete. Geostationary satellites are unable to capture polar regions above a certain latitude, because of the angle.

In addition to geostationary satellites, there are polar orbiting weather satellites:


NOAA-18,-19
MetOp-A,-B (EUMETSAT)


Polar satellites fly much lower (~800 km) and cannot provide continuous global coverage, only swathes along their orbits.

All of this data can be used in the assimilation (initialization) process of weather forecasting models. In turn, one can produce images of cloud cover from the output of the models, see e.g. wettercentrale.de.

NASA operates mostly research satellites, not so much operational weather satellites, although they do cooperate with NOAA on some of the missions. In Europe, the counterpart is ESA, who run some satellites on their own (e.g. Sentinel and in the past Envisat and ERS-1,-2) and cooperate with EUMETSAT.

The data from satellites is downlinked to communication centers (sometimes routed via other communication satellites), where it is processed by various algorithms into products (data files). Product files can be downloaded over the Internet by national weather services or are made available publicly to anyone (all data from NASA satellites is public - see e.g. NASA Global Change Master Directory).

Weather radars are generally located on the ground. They operate by sending short pulses of microwave radiation and measuring the reflected (backscattered) radiation from water/ice droplets. As the microwave radiation has relatively large wavelength (on the order of one millimeter), it is not very sensitive to cloud droplets, and you can see mostly bands of precipitation. Weather radars are operated locally by national weather services. You need roughly one per 250 km to get a good coverage. As with data from weather satellites, they are very important in assimilation of numerical weather prediction models. There are also spaceborne radars, e.g. DPR on GPM Core Observatory, TRMM, or CloudSat.