Either from the circuit schematic which you will probably not have or from the colour bands - sometimes on a burnt resistor the top is burnt but some of the colour is still visible on the underside - you have to unsolder and lift the component to see any remaining colour.
Also - just because it's burnt that does not mean that it's no longer a resistor - lift one end and measure the value.
If this doesn't work for you then take a guess - bung in something around 33K (three orange bands) and see what happens.
As for the burning - either the resistor wattage was under rated and the resistor has slowly burnt with the passage of time - or - something has gone wrong with the circuit containing the resistor and it has been subjected to a higher voltage than normally expected.
A burnt resistor does not necessarily mean a bad resistor - just that it got too hot
If you do go ahead with a new resistor you can put in one of the same resistance value but with a higher wattage rating - physically bigger- to stop the cooking.
Good Luck...
January 2016