You need to make the following Ckt.
On the secondary of the transformer (12V side), you should make a rectifier with capacitor filter. This will give a DC voltage of 12*√2 = 17V. This should be followed by the the regulator IC LM317 or LM7812 which will give DC 12V.
The regulator IC cannot take more than 1A, so you cannot load the IC with more than that load. Even for less than 1A you might need to have a heat sink.
What you are not understanding is that it is not the transformer or the regulator that determines how much current goes through it. The 3A for the transformer and the 1A for the regulator is the MAXIMUM limit. It can handle ANY current BELOW this limit. The amount of current is determined by the load.
Lets say that after the circuit I described, you put a 12 Ohm resistor across the 12Volts output of the regulator, it will draw 1A (I = V / R). This current is the one which will flow through the regulator and the transformer.
If you put 24 Ohms instead, it will draw only 0.5A.
If you put 6 Ohms, it will draw 2A. This will damage the regulator since its limit is 1A.
You have to see what is the current drawn by your fan. It will have this specification on it either as Current itself or as Power and Voltage where you will have to calculate the current drawn by it. (Power = Voltage * Current).
If the current drawn by your fan is more than 1A, you can not use this arrangement since it will damage the regulator.
There are more efficient methods available but they are more advanced.