Old home. From ceiling comes white, ground, red & Black. Everything is controlled by a switch. My fan comes white, blue & black. I understand ground to green and white to white, Should the blue (fan) go with black or red? And the Black (fan) to black or red?

Could be either. Remove switch plate cover and see which wire (red or black) is connected to the switch. Connect the wire that is connected to the switch to the blue of the fan/light.

So this fan has a light kit and or a 3 way switch some where, right?