How do we know the universe is expanding using redshift?

All things considered, based on what I recall from last year, objects closer to us have a more compressed wave length of light, which makes it a higher frequency and looks more blue; objects further away have a less compressed wave length and a lower frequency, which looks more red (lower frequency is red, higher frequency is blue). If objects are getting less blue and more red, that indicates they are moving away from us, and if everything is moving away from us, that indicates the universe is expanding.

p.s. I might have flipped some of the items, so they might actually be the other way around.

When Hubble discovered the red shift in the universe it created a siemic shift in the world view of the cosmos.

The red shift is a result of light waves being spread out as the waves move away from the observer. The spreading out of the waves increases the wave length observed. Red is the longest wave length in the visible spectrum. So the red shift indicated that the universe is moving away from the observers on the earth.

The conclusion from Hubble's observations of the red shift is that the universe is expanded outward from some beginning point in time. This conclusion is consistent with the observations of the red shift through the universe, and the physics of the doppler effect.

Before Hubble scientists believed that the present universe was eternal existing in a steady state. Hubble's observations destroyed this world view. The conclusion is that the present universe had a beginning and matter and energy are not eternal

The redshift of the light spectrum, which is a result of the Doppler effect and indicates that galaxies are moving away from each other and that the space between them is expanding, is how we know the universe is expanding. As galaxies move away from us, their light is shifted towards longer (redder) wavelengths.