Ignoring the upper and lower parts and focusing only on the tapered sides of the cylinder, how can I get a cylinder to have that shape?
I've tried several things:
Add a few horizontal loop cuts and try to scale it in with proportional editing turned on and set to sphere.
Boolean operation - I created a second cylinder, rotated it and brought it in close to the main cylinder and applied a 'difference' boolean operation. It worked - the sides looked like I wanted them to, but the mesh became a mess and I couldn't find a way to fix it. I used the knife tool to connect a few vertices and ended up with a mix of polys and tries that looked terrible.
Tried a few other things that I am embarrassed to admit I did lol.