The first thing we need to do is to remove the power wires from the fan connector, i.e. the first and the second wires.
If there is a sleeving protecting the wires, you will need to open it with a blade or scissors, as shown on Figure 5. Later you will need to cut the portion of the sleeve that will be hanging with a scissors.

click to enlarge
Figure 5: You will need to open the sleeving if your fan has one.
To remove the pins you will need a precision screwdriver (here we used a 1.4 mm one). Look carefully to the fan connector and you will see a small opening in front of each pin. Thru this opening you can reach the lock that holds each pin in place. What we need to do is push this lock with the screwdriver in order to release each pin, like shown on Figure 6. Then just pull gently the wire and it will come out of the connector, like shown on Figure 7.

click to enlarge
Figure 6: To remove a pin from the connector, push its lock with a precision screwdriver.

click to enlarge
Figure 7: Then pull the wire gently.
The third wire must be kept on the connector and you will install the connector back to the motherboard, as shown on Figure 9. If you are modding a fan with 4-pin connector, the fourth pin should be also removed and insulated with insulating tape.

click to enlarge
Figure 8: Our connector after we removed the two power pins.

click to enlarge
Figure 9: Connector installed back on the motherboard.
Now it is time to connect the pins to the power supply.