How to drive a MOSFET with an optocoupler?
The suggested MOSFET is not well suited to this application. 
There is a severe risk that the result will be a smoking ruin :-(.
Principally, that FET is only very very marginally suited to the task. It could be made to work if it was all you had but there are much much much more suitable FETs available, probably at little or no extra cost. 

The main issues are that the FET has a very bad (= high) on resistance, which leads to high power dissipation and a reduced level of drive to the motor. The latter is not too significant but is unnecessary.

Consider - the data sheet says that the on resistance (Rdson - specified at top right on page 1) = \$0.18 \Omega\$. Power dissipation = \$ I^2 \times R\$ so at 6A the power loss will be \$(6A)^2 \times 0.18 \Omega =~ 6.5W\$. That is easily handled in a TO220 package with an adequate heatsink (somewhat better than a flag type preferably) but this much dissipation is totally unnecessary as much lower Rdson FETs are available. Voltage drop will be \$V = I \times R = 6V \times 0.18 \Omega =~ 1.1V\$. That's \$ \frac{1}{24} =~ 4%\$ of the supply voltage. That's not vast but unnecessarily takes voltage that could be being applied to the motor.

That MOSFET is in stock at digikey for $1.41 in 1.s. 

BUT

For 94 cents in 1's also in stock at Digikey you can have the ultra magnificent IPP096N03L MOSFET. This is only 30V rated, but has \$I_{max} = 35A\$, \$R_{DS(on)}\$ of \$10 m \Omega\$ (!!!) and a maximum threshold voltage (turn on voltage of 2.2 volts. This is an utterly superb FET both for the money and in absolute terms. 

At 6A you get \$P_{diss} = I^2 \times R = (6A)^2 \times 0.010 \Omega = 360 mW\$ dissipation. It will feel warm to the touch when run without a heatsink.

IPP096N03L data sheet 

If you want a bit more voltage headroom you can get the 97 cents in stock 55V, 25A, \$25 m \Omega\$  IPB25N06S3-2 - although gate threshhold is getting marginal for 5V operation.

Using Digikey's parameter selection system let's spec the "ideal FET for this and similar applications. 100V, 50A, logic gate (low turn on voltage, \$ R_{ds(on)} \$ &lt; \$ 50 m \Omega\$.

Slightly dearer at $1.55 in 1's in stock at Digikey BUT 100V, 46A, \$ 24 m \Omega\$ \$R_{ds(on)} \$ typical, 2V \$V_{th}\$ ... the utterly superb BUK95/9629-100B where do they get these part numbers from? :-)

Even with only 3V gate drive, at 6A \$R_{ds(on)}\$ will be about \$35 m \Omega\$ or about 1.25 Watt dissipation. At 5V gate drive \$R_{ds(on)} ~=25 m \Omega\$ giving about 900 mW dssipation. A TO220 package would be too hot too touch in free air with 1 to 1.25 Watt dissipation - say about 60 to 80 C rise. Acceptable but hotter than needed. Any sort of flad heat sink would bring it down to just "nice and warm". 

This circuit from here is almost exactly what you want and saves me drawing one :-).



Replace BUZ71A with MOSFET of your choice as above. 

Input:


Either: X3 is the input from the microcontroller.
This is driven high for on and low for off.
"PWM5V" is grounded.
Or: X3 is connected to Vcc.
PWM5V is driven by the microcontroller pin - low = on, high = off.


As shown \$R1 = 270 \Omega\$.


Current is \$ I= \frac{(Vcc-1.4)}{R1}\$ 
or Resistor is \$ R = \frac{(Vcc-1.4)}{I} \$


For Vcc = 5V and \$270 \Omega\$ I here =~ 13 mA.
If you wanted say 10 mA then \$R = \frac{(5V-1.4V)}{10mA} = 360 \Omega\$ - say 330R

Output:

R3 pulls FET gate to ground when off.
By itself 1K to 10k would be OK - Value affects turn off time but not too important for static drive. BUT we wil use it here to make a voltage divider to reduce FET gate voltage when on. So, make R3 the same value as R2 - see next paragraph. 

R2 is shown gointo +24 Vdc but this is too high for the FET maximum gate rating. Taking it to +12 Vdc would be good and +5Vdc would be OK if the logic gate FETs mentioned are used. BUT here I will use 24 Vdc and use R2 + R3 to divided the supply voltage by 2 to limit Vgate to a safe value for the FET.

R2 sets the FET gate capacitor charge current. Set R2 = 2k2 gives ~10 mA drive.
Set R3 = R2 as above.

Also, add a 15V zener across R3, cathode to FET gate, Anode o ground, This provides. gate protection against over voltage transients.  

The motor connects as shown. 

D1 MUST be included - this provides protection against the back emf spike which occurs when the motor is turned off. Without this the system will die almost instantly. The BY229 diode shown is OK but is overkill. Any 2A or greater current rated diode will do. An RL204 is just one of a vast range of diodes that would suit. A high speed diode here may help slightly but is not essential. 

Switching speed :  As shown the circuit is suitable for on/off control or slow PWM. Anything up to about 10 kHz should work OK./ For faster PWM a properly designed driver is required.