I will give you a drawing, but you may need to make some tweaks for your setup.
Will edit this post with an image a bit later today. I have been playing with that since I mentioned it.
This is what I have as a fan controller. I did not built it, but got it with my case.
The variable resistor and the fixed resistor form a voltage divider allowing control from about 4 or 5- tonearly 9 volts(how close depends on the transistor in use. They all have a loss). The resistor divider has very low current and can not even turn over a fan. It can run an opamp or other low power device but not even the lowest power computer fan will work this way. you would need far lower resistance levels and that is why a variable resistor alone is not a great idea.
Now because the wiper on the variable resistor is what sends voltage over the the transistor you get even better range(vs not connecting the other side of the variable to the fixed resistor) because when it is all the way over the the left, you have almost no resistance(nearly full voltage) and a small bit of current will be used in the bottom resistor(it is a small load) and the other side of the variable resistor. Again these higher values are why you do not generate much heat. If you made this with low value parts things would heat up allot.
The transistor has its collector at the positive side of the power supply and gets the voltage from the divider at its base. it will follow the voltage it sees at the base and push the same amount(minus transistor losses) out the emitter. This side is now connected to the fans positive and the negative is connected back to the power supply.
You see the diode next to the transistor. It is to protect the transistor. Please add it. It will not make things work any better, but you still want it. IT should also prevent reverse voltage from damaging the transistor it self. Some will have this built into the transistor. The data sheet can tell you for sure.
I can not stress enough that if you are not comfortable doing this, these devices can be picked up rather cheap online pre made.
I have seen some that use a voltage regulator as well(different design, in this case the transistor sheds the extra voltage. the other setups use a regulator to do it), but even those should work, they just will not go down as low(but most times low enough that your fan would not start anyway).
EDIT..
I would also like to add that you have to ensure you get a decent gain transistor. My cheapies(aka robbed from old devices) are not high enough and require in a darlington pair configuration(2 transistors so that one can make up extra gain current for the next. The downside to this is more voltage loss. this is something you do not want on a 9 volt supply. You will already loose 0.7-1 volt as it is off the top end) to power fans without pulling too much from the base. It is mostly a limit of the voltage dividers limited current.