All of this depends on your budget.
As far as engine mods go, you will want to get rid of the stock intake and get a uni or some type of foam air filter 39-42mm f (approximately 1.5") like this
http://www.sycpowersports.com/index....id=66&incid=29
attach a 6" drain pipe or something similar to the carb with a rubber connector its a 1.5" connection (but it's in mm, measure yours). Then stick the Uni on the other end tighten and done.
then you will have to re-jet the carb probably a 125 (that's where a lot of people start, you may need more are less depending on your elevation/temp/humidity etc...) jet for a gy6...
http://www.sycpowersports.com/index....id=66&incid=29
You can then, upgrade the stock CDI to a No Rev limiting one, you can find them all over the place, check the sycpowersports also.
Once you upgrade the CDI you can upgrade the coil, to one with more spark (orange medum, RED high).
Then there are CVT mods, inside the cover on the left side of the engine is your CVT (or continuously variable transmission). You can swap the rollers for some that are lighter for better acceleration and trail riding (stock is 14grams I think), or get some sliders for added performance (they cost a little more). Also is the clutch, you can swap the stock spring for a 1500 or 2000rpm contra spring (the big one). It will help to downshift the buggy quicker, it will also up-shift slower for better acceleration and hill climbing. The spring and the sliders/rollers have to be matched up for your type of riding and speed.
39T sprocket, you will loose speed but gain low end power.
those are some of the simple things you can do, after that there are big bore heads, upgraded valves, stroker cranks, and many other things. It just depends on what you want to spend and how much more power you need.
in my sig, you can see some of the mods that I have done to my spiderbox.
T.J.