In wing design, how is factor of safety related to G-limits?
Structural Factor of Safety is the margin between the normal limit load and the ultimate load the structure has to take.  It is normally 1.5 times the yield load or limit load of the structure.
The structure is designed to withstand the Limit Load that is applicable to the category, in the case of Transport airplanes 2.5G, without permanent deformation.  The Factor of Safety is applied on top of this value as a minimum, below which the structure may permanently bend, but not break completely.
So an airliner has to be good for 2.5G without permanently bending the wings, with a Safety Factor value of 3.75G before the wings break off, and you have to design your structure taking into account of the elasticity and ductility of the material, to achieve both those requirements.
The Limit Load is the maximum load the airplane is expected to encounter out in the world doing its thing.  The 1.5 Safety Factor been been in use since the 1930s and is a fudge factor to account for all sorts of variables, like assembly defects, calculation errors, aging damage etc.
So to answer your question, although you said 3G, we'll say the value you're interested in is the value for light planes in the Normal Category, which is 3.8G, which would be the design limit load that it's expected to be able to take with no permanent damage.  The Safety Factor, which by industry convention is 1.5, is added on top of that value to get 5.7G and is expressed as design ultimate load for Normal Category. So you have to make sure your wing can take 3.8G and still return to its original shape, and 5.7 Gs before breaking off.
You try to get as close to these limits as you can in your design, because every pound of weight above the minimum requirement is wasted ballast as far as the airplane operator is concerned. However, designers may add additional structure on top of that calculated to meet the regulatory minimum just to be safe (especially if the materials are new), or to improve fatigue life. This is why wing structures typically get tested to failure after their fatigue test program is completed, to see what will happen and to prove they can meet ultimate load requirements, and usually fail well above the design ultimate limit.
You might find this report from the 1950s helpful.