There are usually several simple ways to check if the air filter is clogged. You can choose based on the skills and tools you have at your disposal

Method One: Direct visual inspection (the most commonly used and simplest)
Find the air filter: It is usually located in a square or round plastic or metal housing (air filter assembly) inside the engine compartment. It is connected to the engine air intake through the air pipeline.
Open the housing: Most air filter housings are fastened with clips or screws. Carefully loosen the snap or unscrew the screws to open the upper cover.
Remove the filter element: Take out the filter element inside (usually made of paper, in a cylindrical or folded shape).
Visual inspection
Look at the color: New filter elements are usually light yellow or white. If the filter element becomes extremely dark black, even close to pure black, it indicates that it has adsorbed a large amount of dust and impurities.
Check the degree of clogging: Carefully observe the inside and outside of the pleats of the filter element. If the creases are completely filled with thick dust or the filter paper no longer looks breathable, it can basically be determined that it is clogged.
Compare the old and the new: If you have an old filter element for comparison, the difference will be more obvious.
Smell the odor: Sometimes the filter element may absorb some oil stains or special odors. Smell it to see if there is anything abnormal.
Put back and cover: After the inspection is completed, put the filter element back (if it is for inspection, not replacement), then cover the housing, and fasten the clips or tighten the screws.

Method Two: Touch or feel with your hand
After removing the filter element, gently touch the surface of the filter paper with your hand.
If it feels very thick and hard, or dust particles can be clearly felt, it indicates that the blockage is quite serious.

Method Three: Check against the light (to judge the breathability)
Place it in a well-lit area or shine a flashlight on the filter element.
Observe whether the light can pass through the filter paper. If light can hardly penetrate or only a small amount of light can pass through, it indicates that the air permeability of the filter element is already very poor and it is severely clogged.

Method Four: Judging based on Vehicle Symptoms (Indirect examination)
Although this is not a direct inspection of the filter itself, when a vehicle shows the following symptoms, it often indicates that the air filter may be clogged
Weak acceleration and slow speed increase.
The fuel consumption has increased significantly.
The engine shakes, is unstable and may even stall at idle speed.
While driving, the vehicle felt suffocated and it was particularly difficult to go uphill.
The engine is overheating.
The color of the exhaust gas is abnormal (such as black smoke).

Important Notice
Safety first: Before operating in the engine compartment, make sure the engine has cooled down to avoid burns. If disassembly is necessary, it is best to park the vehicle on a flat ground and apply the handbrake tightly.
Do not rinse with water: Unless the filter element is of the washable type (but most car air filter elements are made of paper and cannot be washed with water), rinsing with water will damage the structure of the filter element and cause it to lose its filtering capacity.
Inspection interval: It is recommended to conduct inspections in accordance with the mileage or time suggested in the vehicle maintenance manual. When driving in an environment with a lot of dust, more frequent checks may be required.
When unsure: If you are not sure whether the filter element needs to be replaced, it is best to consult a professional auto mechanic.

By using the above methods, you can relatively easily determine whether the air filter is clogged, and thus decide whether it needs to be cleaned (if possible) or replaced with a new filter.