Will the sun eventually die one day and if so what happens to planet earth next?

It is thought that when the Sun becomes a red giant, that it will expand out to about where the orbit of Mars is now. It is also thought that this is approximately where the Earth will be orbiting when the Sun becomes a red giant. So in all likelihood, the Earth will be swallowed up by the Sun and will not survive the red giant phase. If it somehow does, it will be burnt to a cinder and will continue to orbit the Sun after it becomes a white dwarf. It will basically be a dead, cold, burnt-out rock. 

The Sun will become a white dwarf star one day. If the?Earth and Moon survive the Sun's red?giant stage and the helium flash when the Sun tries to fuse the hydrogen in the shell around the Sun's core. The Earth and Sun will continue to orbit the Sun and will be totally locked to each other like Pluto and Charon on are totally locked. 

Planets DO survive the helium flash. The first confirmed exoplanets were orbiting a white dwarf pulsar.

The Sun will very slowly become?a black dwarf star. That will take a trillion years or more. 

The Sun does NOT HAVE?ENOUGH MASS to go supernova?and explode. 

NO ONE KNOWS how much the Sun is going to expand during the red giant stage. NO ONE. 

Yes.  About a billlion years before the sun dies, the Earth will be a hot, lifeless rock.

Earth will be burn out by the sun before it dies. Part of a suns life cycle is becoming a red giant. When our sun does this many millions of years in the future it become so big it will destroy all life on Earth. 

Unfortunately it will explode and destroy Earth and the rest of the solar system.