Some problems announce themselves and some have to be checked. A bathroom exhaust fan exists to remove moisture from the room before it settles on the mirror, the paint, the ceiling, and the window frame. If that moisture is still there long after the shower, the fan is not solving the problem, whatever the switch says.
The signs that the problem is still there
Start with the mirror. After a shower with the fan running, the glass should clear within a short while. If the mirror stays fogged for long stretches, the air is still holding its moisture. Look at the walls and ceiling near the shower as well. A dull patch, a soft spot in the paint, or a damp feel at the corners tells you the room is not drying out between showers.
Check the window. Condensation that runs down the glass in colder months points to humid air with nowhere to go. Then check the smell. A room that still feels damp long after the shower is holding moisture.
Check whether the fan is moving air
Turn the fan on and hold a square of tissue near the grille. The tissue should be pulled toward the opening. A tissue that hangs still means the fan is not moving air at the grille. Confirm that the switch, or the timer switch if the room has one, actually starts the fan. Listen during the run. A fan that stays silent with the switch on has a problem before it has a performance question. Look up at the grille from below for dust and lint, which also cut airflow.
Record what you find before you act
Write down what you saw: how long the mirror stayed fogged, whether the tissue moved, whether the fan made sound, and whether the grille was clear. That note tells whoever you call what to check first. It also shows whether the problem is the fan, the duct run, or the room itself, and that difference decides whether you need a cleaning job or a planning decision.
Turn off the power at the switch before you open the grille or reach into the housing. The fan is wired to the house circuit, so leave any wiring work to a qualified electrician.