From the ceiling I have two romex wires (black and white each), one from the wall switch and another. From the fan I have a black, white, and a black/white wire. Previously the lights were controlled from the wall switch and the fan speed from the fan pull switch. I would like to keep it that way. What are the proper connections?

Additional info: when I took down the old fan, it wasn't properly mounted from the ceiling and it pretty much fell into my arms before I could identify the old connections, but it seems that a black from one romex was twisted with the white of the other romex as it comes down from the ceiling. Is that right? Also,I have a proper mounting brace in the ceiling now.

That is a switch loop, Ceiling black to white from wall switch, black back from wall switch to black and black/white on fan, ceiling white to fan white.

First remove the switch cover plate and make sure you have only one black and one white wire in that box.

You then need to determine which cable in the ceiling is the power in cable and which is the cable to the switch. If one of the white wires has a piece of black tape on it, that will be the cable to the switch. If neither white wire has the black tape and if you have a meter or voltage sensor, do a voltage check (with power on) between the black and white wire of each cable. Put a piece of black tape on the white wire of the cable to the switch.

If you do not have a meter, turn the power off and connect the black with strip wire from the fan to one of the blacks in the ceiling. Connect the white from the fan to the white in the same cable. Turn the power back on. If the lights burn you have connected to the power in cable. If the light do not burn you have connected to the switch cable. Put a piece of black tape on the white of the switch cable.

Now connect the white with the black tape, and the black in the other cable, and the black from the fan together. Connect the black with the white strip from the fan to the other black. Connect the white from the fan to the other white.