NOAA (National Oceanic and Atmospheric Administration, to give it its proper name), is an agency of the US government, not a private company.
Satellites are just the vehicles which carry the sensors into orbit. Microwave radiation from the atmosphere is used to estimate the amount of water vapor.
The satellites have instruments to detect many different portions of the EM spectrum. Water vapour is often detected in the 5 - 8μm range.
If you create a free account on this website: http://www.sat.dundee.ac.uk/
you can retrieve satellite images from many different platforms in near real time and also browse the archive.