Step 1-- Tropical Wave: "bump" or disruption of normal tropical easterly flow. Associated turning of wind causes low-level convergence of air; which helps with falling pressure and enhanced showers.
Step 2-- This can evolve into a Tropical Depression, which is a closed circulation of air in the low levels. This in turn increases convergence and pressure falls, and wind speeds increase in a Catch-22 effect (i.e. the stronger the wind blows the greater the convergence, the quicker the pressure falls... so the stronger the wind, etc.).
Step 3-- Once sustained winds reach 39 mph in the closed circulation a Tropical Storm is named. Usually there are at least 2 closed isobars of 4 mb increments around the center. If atmospheric conditions remain correct the system will evolve into a...
Step 4-- Hurricane. There is usually a difference in pressure of at least 0.60 inches of mercury between the center and surrounding pressure field, with the greatest change near the center (eyewall). It is this great difference in pressure, which sometimes can be as great as 2.95 inches of mercury, that causes the wind to be so strong.
Step 5-- A mature hurricane is a well-oiled meteorological machine, but disruption of the processes that drive the storm (i.e. interaction with land or colder air feeding in) will begin to destroy the storm, and the disintegration of a hurricane can often be quick and dramatic.