The conserved quantity is derived from Noether's theorem itself. One thing that is a bit hairy is that Noether's theorem only applies to a continuous, smooth (physical -> there is some wiggle room here) space.
When deriving the conservation of energy from Noether's theorem you basically say that your Lagrangian (which is just a set of equations that describes a physical system) is invariant over time. When you do that you automatically get that energy is conserved. Each invariant produces a conserved quantity as explained in parent comment when you apple a specific transformation that is supposed to not change the system (i.e remain invariant).
Now in doing this you're also invoking the principle of least action (by using Lagrangians to describe the state of a physical system) but that is a separate topic.
When deriving the conservation of energy from Noether's theorem you basically say that your Lagrangian (which is just a set of equations that describes a physical system) is invariant over time. When you do that you automatically get that energy is conserved. Each invariant produces a conserved quantity as explained in parent comment when you apple a specific transformation that is supposed to not change the system (i.e remain invariant).
Now in doing this you're also invoking the principle of least action (by using Lagrangians to describe the state of a physical system) but that is a separate topic.