Time frame is very dependent on your home.
If you have pets near the computer, outside environment, how sealed your house is all play a factor.
I have seen computers filthy in 2 months, and others with almost no dust 4-6 months latter.
Power off the system and run a can of compressed air through it. Make sure to take a pencil or other slender object to block each fan from moving when you spraying it, this includes the case fans, cpu fan and PSU fan.
If you have a higher end case you may have air filter (s) on the intake fans.
As stated if using compressed can air dont tilt it and still even at that give it 5 to 10 minutes before powering back on the computer.
It is not advised to use air form an air compressor unless you understand what aspects make it dangerous and correct those aspects (like risk of moisture in line, over pressure, etc)