describe how the national weather service monitors an approaching hurricane and how it informs the public about this impending servere weather.

A wet barometer puts a vacuum above a liquid and applies air pressure to the surface of the liquid - the height of the liquid above to reservoir surface is the measure of air pressure. The liquid can be in a J tube with an open end or a straight tube in a pool. Air pressure will support about 30" of mercury or about 32 feet of water. 
A dry barometer uses a sealed chamber with a diaphragm with a lever touching it or a spiral tube with a link connected to a display needle. In the former, the slight movement of the diaphragm with changed pressure is translated to a large movement of the end of the lever movement across the scale. In the spiral, the expanding/contracting air inside the tube changes its shape and pulls the needle over. 
In both case, the scale of pressure for the needle has to be calibrated to the design. 
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How Tropical Cyclones are Observed 
* Direct measurements of tropical storm and hurricane dimensions and wind speeds are taken primarily by reconnaissance 
aircraft, although ships and buoys also take important measurements. Once a hurricane is near and/or on land, Automated 
Surface Observation Systems (ASOS) provide surface conditions, and radio sondes take upper air measurements. 
* Indirect observational methods include satellite imagery and Doppler radar. In particular, satellites have greatly improved 
our ability to monitor and understand hurricanes. Radar data are important once the storm comes close to shore 
and after landfall for forecasting hurricane-related weather. 

I hope this is helpful.