I take it that you'd be using the GPIOs PWM function to generate pulses to toggle the LEDs quickly on and off to control the light level.
You can connect the gate (G) of the FET to a GPIO. The source (S) to the negative output of the power supply and the led strip between the positive and the drain (D).
Of course you'll have to connect the negative terminal of the power supply also to the GND of the Raspberry Pi.
simulate this circuit – Schematic created using CircuitLab
I've added an optional resistor (R1) in the schmatic that will discharge the gate if the GPIO is in high-impedance state or disconnected. This prevents the FET from staying "switched on".
Another optional resistor (R2) limits the momentary current when switching the FET on or off. (See comments).
Also worth mentioning is that the FET you've chosen (FQP30N06L) has low enough gate threshold voltage (VGS(th)) that it probably will work ok with the Pi for this application. Certain other FETs with higher VGS(th) might not work at all. For example this 30N06L from Unisonic possibly won't.