How to check issue with gas fireplace?
It's difficult to help you troubleshoot a device, without a bit more information about it. Since you're not giving us much, I'll try to give general advice.
Depending on the system, there's a few things that could be wrong.
Gas Valve Closed
This would affect every type of gas fireplace.
Test:

Locate the gas valve.
Turn on the switch.
Listen for the valve to open.

If you hear the valve open (click, clank, clunk, etc.), but don't hear or smell gas. The valve may be off.
Most gas valves are quarter turn ball valves, so you can tell when they're open simply by looking at the knob.  The knob should have an arrow, handle, or other linear feature on it. This feature should be aligned with (parallel to) the pipe, when the valve is open.
Solution:
Turn on the gas.
No Gas
If you get your gas from a tank or bottle, you'll want to make sure you have gas.
Test:
Similar to above, except that the valve will be open.
Solution:
Fill the tank.
Bad Switch
Since the system relies on a switch to know when to turn on, a bad switch could be devastating.
Test:

Label and remove the wires from the switch.
Test continuity across the switch, in both positions.

When the switch is toggled on way, you should measure infinity (or not hear a beep). When the switch is toggled the other way, you should get a measurement (or hear a beep).
Solution:
Replace the switch.
Pilot Not Lit
If your system requires a pilot, and it's not lit. You can flip the switch all you want, you'll never make fire.
Test:

Look at the pilot.

If you see a flame, it's lit.
Solution:
Light the pilot.
Bad Flame Sensor
Fireplaces use flame sensors (thermocouples, thermopiles, etc.), to determine if there's a flame. If the sensor goes bad, the system will not hold the gas valve open.
Test:

Disconnect the thermocouple from the system.
Set multimeter to measure DC millivolts (mV).
Connect the black lead to the button of the thermocouple.
Connect the red lead to the copper part of the thermocouple.
Heat the thermocouple with a torch.


As the thermocouple heats, you should get a reading on the multimeter.
Solution:
Replace the flame sensor.
Bad Gas Valve
If the system is getting all the right signals, but the gas valve is not opening. It could be a bad valve.
Test:
See test for Gas Valve Closed. You won't hear the valve open. You'll have to be sure the valve is getting the signal to open, so make sure all other items check out first.
Solution:
Replace the valve.
Depending on the type of fireplace, the ignition sequence will be a bit different. using the typical sequences below, you might be able to narrow down where the problem is.
Typical Gas Fireplace Ignition Sequence
Pilot

Switch is flipped
If pilot is lit (checked via a thermocouple or other flame sensor).

Open main burner gas valve.
Wait (There may be an adjustable timeout, or a hard set timeout).
If main burner lit (check via another thermocouple or other flame sensor).

Leave main gas valve open.


Else

Close main gas valve.
Purge system (in the case of a fireplace, this is likely a timed wait).
Retry ignition (this may happen 0 to many times, depending on the system).




Else

Do nothing



Electronic Ignition with pilot

Switch is flipped
Open pilot gas valve.
Initiate electronic ignition device (spark gap, hot surface, etc.).
Wait.
If pilot flame sensed.

Open main burner gas valve.
Wait.
If main burner flame sensed.

Hold main gas valve open.


Else

Close main gas valve.
Purge system.
Retry ignition.
If no ignition after retries

Close pilot gas valve.
Lockout (this may require something to be physically reset, or a simple timed lockout).






Else

Close pilot gas valve.
Purge system.
Retry ignition.
If no ignition after retries

Close pilot gas valve.
Lockout.





Electronic Ignition

Switch is flipped
Open main burner gas valve.
Initiate electronic ignition device.
Wait
If flame sensed.

Hold main gas valve open.


Else

Close main gas valve.
Purge.
Retry.
Lockout.