I fly a B757 with technology representative of most modern airliners flying today (in terms of 'weather sensing' ability)...although it is an old design!
We have a temperature probe which measures the temperature near the nose of the aircraft. As we're moving through the air at speed, what is measured is actually higher than the actual atmospheric air temperature due to our forward motion - computers on board correct for this and calculate the outside air temperature then display it.
The aircraft can also calculate the approximate wind direction and speed at it's current position by taking information from the inertial reference units and other sources.
We also have a weather radar which picks up reflections from moisture (usually) in the air, sometimes hundreds of miles ahead of the aircraft. Different intensities of radar return display as different colours and from this, their range, shape, what we can see out of the window (!) etc. we can try to interpret what the returns might be e.g. a thunderstorm, a rain shower, ground returns, etc.
Linked to the above is a windshear detection system - this uses the weather radar and other signals to warn of possible windshear ahead of the aircraft.
All of the above is standard equipment on airliners. Certain items/systems above may be required to be operating before departure, others may be OK to dispatch with broken (but operational conditions might apply, for example).
Sory if this is a little too basic for you!