The Earth moves through space at 67,000 MPH. The Milky Way travels through a local group at 2,237,000 MPH.
Wouldn't you need a fixed point to be able to measure velocity against? After all, compared to the total speed of our Milky Way, the Earth isn't moving through space. What fixed points do we compare against? When we say the speed of light is $c$, what is that relative to?
Answer
There are two separate questions there. The easiest one to answer is how we measure the velocity of the Earth, Milky Way etc, because we measure it relative to the cosmic microwave background (or CMB).
If you measure the CMB in all directions and find it's the same in all directions then you are stationary in comoving coordinates. However if you find the CMB is blue shifted in one direction and red shifted in the opposite direction then you know you're moving relative to the comoving frame, and the change in the CMB is due to the Doppler shift. From the size of this change you can calculate your velocity. Measurements of the CMB from the Earth show exactly this Doppler shift, and that's how we can work out the velocity of the Earth. Having got this we can convert velocities measured relative to the Earth into velocities measured relative to the comoving frame.
There are traps for the unwary here, because all velocities are relative and the comoving frame is in no sense an absolute way to measure velocity. It just happens to be a useful reference and one that tallies what our instinctive interpretation of velocity relative to the rest of the universe. This is discussed in the question Assuming that the Cosmological Principle is correct, does this imply that the universe possess an empirically privileged reference frame?.
Lastly back to light. The velocity of light is special because every observer who makes a local measurement of the speed of light will always get the same value of $c$, regardless of what their velocity is. This is one of the building blocks of special relativity.
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