I'm a bit confused as to the ordering of events leading to Sauron's demise at the end of the second age. 

From the Silmarillion it appears that Sauron was hewn down by Gil-galad and Elendil, and afterwards the Ring was cut from his dead body's finger by Isildur. Is this the correct order of events? Or was Sauron weakened by Gil-galad and Elendil and then Isildur cut the ring from his living body causing it to be destroyed?