Just to add to Undo's answer, after the expansion to a red giant, the sun will become a planetary nebula, where (according to the link) the fusion reactions inside the star are 'overtaken' by the gravitational collapse, in turn causing the inner layers to condense and heat up causing the outer layers to be blown away. After which, the hot core forms the remnant, a White Dwarf star (NASA source), which is likely to last for several more billions of years.
The image below depicts the current ideas of the expected lifecycle and timeline of the life of the sun:
How do we know what will happen to the sun?
Currently, the main method to determine the solar lifecycle is described by the article "The Future of the Sun" (Cowing, 2013) is to:
Studying stars with the same mass and composition as the Sun, the so-called "solar twins," can give us more information about our own Sun; solar twins of various ages offer snapshots of the Sun's evolution at different phases
Where the mass and chemical composition of a star provide the information needed to determine its lifecycle.
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