An Empirical Formula is one that gives the simplest whole-number ratio of atoms in a compound. To determine that, we need to convert the mass to moles; this is done using the Atomic Mass Unit values found on the Periodic Table. For sodium, its 22.99 amu; for chlorine, its 35.45 amu. The amu also tells us the molar mass, or the number of grams of each element to make a mole of that element, so for sodium it's 22.99 g/mol, for chlorine 35.45 g/mol. So to find out the number of moles for each element:
moles Na = (6.53 g) / (22.99 g/mol) = 0.28 moles
moles Cl = (10.07 g) / (35.45 g/mol) = 0.28 moles
Now to figure out the ratios of atoms in the compound, you would divide each mole value by the smallest calculated mole value; since the mole values are identical in this case, it comes out to 1:
(0.28 moles) / (0.28 moles) = 1
So there's 1 mole of Na for each mole of CL, and so we have NaCl.