The two fans have different purposes:
The big fan provides cooling air for the main radiator. It is the one that runs when the engine needs more cooling.
The small fan is for the A/C condenser, it runs when the A/C is active. To make it run (or see that you have a problem) turn on the A/C and put the fan at a non-zero speed. The fan should start running at its slow speed.
On the Mk5 (and later?) cars this means setting a low temperature and making sure that the A/C in not in ECON mode. The fan will only run when temperatures are above freezing and if the A/C system is charged with refrigerant.
So, first thing to do it stop make sure that the small fan should be running by ensuring that the A/C is on. Then if it isn't running:
Test the fan - try turning it by hand to see if it is free, then pull the connector and apply power directly to the fan to see if it runs, you could also meter it to see if the circuit is open. It seems that a common failure on these fans is for a brush to hang up and wear to the point that it no longer makes contact. If that's your problem, this video may help if you want to try your hand at repairing it. Otherwise replace the fan. It's not too hard.
If the fan is good then the problem is either that the A/C needs servicing or that the fan control module has failed. If you A/C isn't blowing cold that's where I'd start.