How Do we know about redshift?
Okay so scientists use the red shift to know that galaxies are moving away from us faster than light. How do we know that its not just red light from red stars. i mean most stars are in the infrared spectrum.
Note that red shift occurs for any movement away from the observer; it does not imply motion faster than light. It's just the Doppler shift, which you can also observe in the usual examples of a car horn or train whistle from a vehicle moving past you: its pitch is higher as it comes toward you (with light this would be a blue shift) and lower after it passes you and is moving away (with light this would be a red shift).
Let's start with a quick clarification: Red Shift is not the same as red light.
Red light is just electromagnetic radiation with a 400–484 THz frequency range, the lowest our eyes can see - highest being violet light, with a 668–789 THz frequency.
Red Shift is an observable effect when you analyze the spectroscopic signature of an electromagnetic radiation source that is so far from us that the expansion of the universe (whose unit of measurement is called the Hubble Constant) is noticeable because of the frequency drop, called Doppler effect.
In short, it works like this:
Pick one of the elements the universe is made of - hydrogen (75%), helium (24%) and trace amounts of everything else (1%). For this example, let's stick with hydrogen.
Determine the spectrum signature of hydrogen by running the light generated via electric discharge on the gas through a spectrometer:
You'll notice some markings as you examine the light dispersed by the prism. Those markings are called narrow bands, and they appear as a consequence of quantized energy states. Hydrogen narrow bands are well known : 656.2, 486.1, 434.0 and 410.1 nanometers.
Now look at the sky. Pick any bright dot, run its light through a prism, and knowing that it is also made of roughly 75% hydrogen and 24% helium compare its spectroscopic signature to the bands you obtained earlier.
Because of the Doppler effect caused by the expansion of the universe the light waves are stretched, making the frequency drop - shifting the whole spectroscopic signature towards lower frequencies. The further the object is, more noticeable the shift towards red is.
Thus, the term Red Shift.
Now, answering your question:
How do we know that its not just red light from red stars?
Because even regular light from red stars will shift towards the infrared side of the spectrum as a consequence of the Doppler effect.
Spectral Lines of chemical elements
Stars consist of similar atoms and molecules that we can find here on Earth.
Radiation from those atoms and molecules often occurs at discrete, identifiable wavelengths that form a unique pattern. This is a consequence of quantum physics - the energies of atomic and molecular states are quantised, and radiation arises from transitions between these. These wavelengths can be measured (in a laboratory) so that we know the rest wavelengths of light emitted by atoms and molecules.
When we look at the spectrum of light from a star (or a Galaxy made up of stars) we identify atoms and molecules from the pattern of absorption (and sometimes emission) lines and can work out whether the whole pattern has been redshifted.
Occasionally, the difficulty you propose does occur. Galaxies which emit a high proportion of their light in the form of a smooth continuum (e.g. some types of active galaxies, where the light is dominated by the surroundings of the black hole at the centre) can exhibit a featureless spectrum or with perhaps a single identifiable emission line. In those circumstances it can be impossible to estimate a redshift.