Most common questions used to investigate
Is the compressor engaging?
Check the refrigerant level, is it almost empty?
Is there air blowing through the vents?
Is the air blowing weak?
Common conclusions
There might be a AC refrigerant leak in the system. You can check for it yourself by checking the lines of the air conditioning system. If there are oil residue in some of the joints of the hoses. Or there might one hose that's cracked and leaking. You need to take your car to the air conditioning specialists and have the offending parts replaced. If too much refrigerant leaked out, you might need a full AC recharge.
Go take it to an air conditioning specialist, you need a full AC refrigerant charge, and also maybe ask for an inspection of the AC system, as there might be a serious leak. If the refrigerant is almost empty or already empty, it will prevent the compressor from engaging.
The in-cabin air filter might be too dirty. The in-cabin filters of most cars are usually found under the dashboards, in the passenger side of the cabin. Take it out vacuum it thoroughly, and then put it back. This should allow more air to flow through the airconditioning system.
There might be a problem with the climate control module. There might be an electrical problem with the control module, take your car to a automotive electrician to find out what might be wrong with it.
The blower fan, which is the part that blows air through the system and out through the vents in the cabin, might be broken. The fan could just be stuck, or the motor might be fried and needs replacement.
References
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