If you have a blue wire on your ceiling fan, you must have a light kit included or can add a light kit to the ceiling fan at a later date.
1st of all make sure power is off to that source.
The BLUE wire is for the light.
You are correct that the green wire is for the ground from your ceiling. Connect those two together.
Your WHITE fan wire will go to the WHITE wire from the ceiling
The BLACK fan wire to the BLACK wire from the ceiling.
If you have a RED wire coming from your ceiling hook the BLUE wire to the RED.
If there is NO REd wire from the Ceiling. Your blue wire will get hooked up with the Black wire.
But there will be only one switch to control the lights and/or fan part. You can turn the switch on from the wall. And manuel turn on and off the light or vise versa.
Hope this helps. Need anything just let me know.