What are the best ways to improve gas mileage for a silverado SS? And, how will they effect the performance?  

Well, let's consider what GM did from the factory on its new XFE truck & SUV models. Taller gearing, a tonneau on the trucks, and slightly lower ride height. But with the Silvy SS, you are talking about a 6.0 and AWD. You could do taller gearing and a tonneau, but changing the gearing on an AWD is a real PITA, and I ain't talkin' flatbread.    

Yep, I've got to agree with Ed, since changing gears on an AWD truck means two sets of ring and pinion gears. We did a gear swap in a 2007 Silverado 4x4, and although the front differentials are different, you can see the tech article HERE
On the plus side, your 6.0L has tons of torque, so it should still be able to cruise very well in OD with the taller gears. Another thing the XFE trucks did was use smaller wheels, for less rotating weight. So, if you aren't concerned with your SS looking its best, a set of 16s might be in order.  

Depending on your Milage, a good tune up is the key to regaining your Mpg.  Not to mention performance gains.  

You could do 16s on an SS, but I think it might look a little goofy. Sure, it'd work, but unless you painted them red or flat black, 16s on an SS would look dorktastic. I'm sorry, I'm usually all about function over style, but I think this is where I might have to draw the line. Heck, even I have 17s on my Mazda Protege!

Actually, if you went with an old-school style wheel, you might be able to get away with 16s. Like some old-school Cragars or something like that. Problem is, a lot of the newer trucks have shallow offset, and a lot of the old school wheels are deep-offset. Just a thought. Personally, since it had factory 20s, you might be able to go down to an 18 without looking too weird.  

Changing the gears in your truck should not even be an option considering the cost of doing it. And if you keep the factory gears and get smaller wheels and tires, the gas mileage will go down due to the engine turning more rpm's because when u put smaller wheels and tires on a vehicle, u change the whole gear ratio. If u got larger wheels and tires, it would be more weight but you will change ur gear ratio in a way that the miles per gallon will change.

But overall, if i were u, i would keep the same size wheels and tires and add dual exhaust, cold air intake, power programer, trodle body spacer, mass airflow sensor, headers, etc., etc. All these things will give u better mpg