Hi Arron.
So the TUNE button is used when the ATU/100 is in the NonAUTO mode to set it to tune your Setup for your radio. Press this till the TUNE shows on the display, then key the mic and send a signal to get the tuner to work.
The AUTO button switched between AUTO and NonAUTO. When in AUTO mode Keying the mic and sending a signal makes the ATU/100 tune automatically IF the setup is not already in tune. this can happen often if your setup is not stable, or you are using a big band, as the SWR will change as you go from one end of the band to the other.
The BYP button bypasses the ATU/100 so it will not tune at all. For use when you have a tuned antenna fitted.?
I'm sure others will offer more in depth help here, but hope this helps a little
Vaughn