Just wondering how to find the atomic radii of NaCl
This is what I have so far:

Volume of NaCl (cm^3) 3.97
Density of NaCl (g/cm^3) 2.16
Molar Mass of NaCl 5.84E+01
Mass of NaCl Unit Cell (g) 3.88E-22
Volume of NaCl Unit Cell (cm^3) 1.80E-22
Edge Length of NaCl unit cell (cm) 5.65E-08
Edge Length of NaCl unit cell (pm) 565
Length fof Diagonal (pm) 978

But the radius of the ion a cation are different so how do I go about calculatin each of them? Should I have done something different in my procedure?

From the numbers you are showing, I'll assume you started with the following knowns:
Volume, density and molar mass of NaCl

You're calculations were OK down to the point that you calculated the diagonal. You calculated the diagonal of the cube that represent the unit cell, you should have calculated the diagonal of the face of the unit cell. That's because NaCl is face centered. If you were dealing with a crystal that was body centered, then you would used the diagonal of the cube.

If you calculate the diagonal of the face of the unit cell, you can divide that by 4 to get the radius of Cl.

To get the radius of Na in a NaCl crystal, subtract twice the Cl radius from the face length, and then divide that number by 2.

You are correct that the radii of the ions in the crystal are different than their atomic radius in elemental form. A cation will have a smaller radius in ionic form, and an anion will have a larger radius in ionic form.