It will continue as a fairly normal star for about 5-6 billion years, getting progressively hotter and larger. Eventually and gradually, the outer layer of the Sun will be boiled off, leaving only a very hot core, which will form a white dwarf star. The white dwarf will simply cool off over billions and billions of years.
Scientists know how long the sun will live based upon mathematical predictions of nuclear fusion rates due to the mass of the sun as well as some fluid dynamics.Putting all of these together, we can guess how much 'fuel' the sun has to burn as well as how quickly it burns. With those values, we can guess how long the sun will live.
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