Light is a bit like sound - it travels as waves, and the distance between the crests of those waves will determine the colour of the light or the pitch of a musical note. If you travel towards the source of the light or sound, you encounter the wave crests at a faster rate, and this will shift the colour of the light a little towards the blue end of the spectrum or make the note sound higher pitched. If you move away from the source of the light or sound, the opposite happens, the colour being shifted a little towards the red end of the spectrum or making the note deeper pitched. If a star or galaxy is moving away from us, it's light will be shifted towards the red end of the spectrum, and the faster it's moving away, the further towards the red end it will be shifted.
The result of this shifting might be that a greenish star will look slightly yellower, but the apparent colour by itself won't tell you if it's moving away from you or not if you don't know what colour it should be. So, what you need to do to work out how much the light has been shifted, and in which direction, is look for absorbtion lines in the spectrum of its light which can be identified as relating to specific elements. [Note: I think it's absorbtion rather than emission of light at certain frequencies, but I may have got this the wrong way round, so check before you use this information for anything important.] If you can identify a specific line as relating to a specific element, you then know which part of the spectrum that absorbtion line should occur at if the object wasn't moving, so the actual location of that absorbtion line in the spectrum of the light coming from that star/galaxy will directly indicate how much it has been red (or blue) shifted away from its true position.