I am guessing that you actually mean "kilojoules per mole" and "joules per gram", so the question probably ought to read "How do you convert kJ / mol to J / gram?" (I have put in the "divided by" signs).
In order to answer the question you need a third piece of information: "grams per mole" or "g / mol". This is sometimes called the molecular weight of the substance, or (better) the "molar mass" of the substance. As an example, the molecular weight of water (H2O) is roughly 18 grams per mole. This is because each Hydrogen atom has a mass of approximately 1 gram per mole, and each Oxygen atom has a mass of approximately 16 grams per mole. 2H + 1O = H2O.
So if the number of kilojoules per mole is "X" and the number of grams per mole is "Y" then
X kJ/mol รท Y g/mol = X/Y kJ/g = 1000X/Y J/gram