A tip for you is this - stretch the spring out and test bend it into a circle. Keep doing this until you got a big enough circle. Then, join it. See how it fits under the lamp. You want it to be the same size as the bottom, just a tad smaller though because the glass is about 1/8" thick. It will be bigger than the spring in there for sure, but too big and it won't fit the bottom. You will see - really easy :)
Your spring question - I just stretched them. You don't outright stretch them as hard as you can, you just do it a little at a time. Keep doing it until you have a good amount of spacing between the springs and when you bend it to make the circle, make sure its the correct diameter. If it gets too big, compress the spring back together. Will take a couple tries to squish it back in case you stretch it too much so try not to do that. Other than that, pretty easy.
1 pack does 2 lamps (2 springs per pack). Which reminds me, I forgot to go get new springs. :)