I'll be replacing the stick box on one of my original gc controllers soon, I don't wanna replace it since i consider them sort of antiques as they came with my two gc's (I have a purple and black one, the black one is all the way back from 01). Its def not easy to do if you've never done soldering. The 10 points you have to remove solder from are small and fine(If your on one of the older controllers, the newer ones have 4 less). You have to use one of the smaller solders irons and have your arm resting and very calm. Or else you'll end up making a mess and burning the board along with bringing dirt into the solder if not properly cleaned beforehand.
If you want something to reference to, this is the video to look at:
You'll need a soldering iron to heat it up, and something to suck out the solder, either what he is using, or the other option he mentions where it uses a latched pump to suck it out.
If your still up for it, these guys sell a replacement stick(They usually sell these things in pairs at least):
Ebay
Ebay(2)
Aliexpress(2)
Buying in bulk is cheaper(Only do this if you get requests from others/plan to do this in the long term):
Amazon(6)
Ebay(6)
Amazon(10)
Aliexpress(30)
One of the nice things is once you've successfully done this, the process is mostly the same for any other modern controller. So if you have dead sticks in something like your ps3 controller you could do the same thing.
As for the buttons, so long as the plastic is still in its correct shape all you would have to do is replace the acutal rubber pad underneath as it may just have worn out and lost its tension.
Again, they sell these in sets for the entire controller:
Ebay
Amazon
ZedLabz
Bulk:
Aliexpress(5)
Aliexpress(10)
Aliexpress(30)