How is ocean salinity measured from space?
In a nutshell:


The instrument measures microwave radiances (after calibration)
If we know the sea surface temperature, we can use radiances to calculate emissivity.
The emissivity at 1.4 GHz is itself a function of near-surface ocean salinity.


However, in reality, it's more complicated, because there are other factors that come into the equation, such as surface roughness, which depends on wind.  Remote sensing problems are often underdetermined, and we need to make assumptions in order to retrieve the desired quantity.  Measuring ocean salinity from space is a classical inverse problem.

You can find details in the highly cited paper:


  Kerr, Yann H., Philippe Waldteufel, J-P. Wigneron, J. Martinuzzi, Jordi Font, and Michael Berger. "Soil moisture retrieval from space: The Soil Moisture and Ocean Salinity (SMOS) mission." Geoscience and Remote Sensing, IEEE Transactions on 39, no. 8 (2001): 1729-1735. (weblink).


which addresses both soil moisture and ocean salinity.