What I do is I use canned air, and at least partially disassemble the computer to the point I have good fan access to get rid of the majority of the dust, just to make things easy for ones which aren’t too far in the dusty range disassembly is justified. However, if I don’t know if the machine has been maintained, or I got it used I am a bit more through.
What I do on machines I know haven’t been maintained or cleaned in years is I will usually take the fan off of the heatsink assembly, when possible*. After I do that, I blow the fan out separately from the computer and then focus on just dealing with the dust bunnies in the heatsink fins. Depending on the age of the machine, I also repaste it.
*The exception is machines like the AMD 8690M+HD 4600 E6440, which requires heatsink removal to get the fan out of the machine. For these, I usually just knock out most of the dust and do the real cleaning when I repaste these systems. The HD 4600 units with the easily serviced fan and heatsink are units I unscrew the fan on, blow canned air at the fins and then I may repaste if it makes sense - although there ARE ones with the same “sealed” fan assembly without the GPU footprint. You can quickly spot them if you have a lot of experience, thankfully - they mirror the 8690M dual GPU heatsink without the cooling footprint those have for the GPU.
For example, on a machine like this I usually remove the bottom and I’m okay to blow the fan out (E6440 with the easily removed fan):
However, if I need to go further I’ll find the path of least resistance to expose the fan so it all leaves and doesn’t get trapped. I usually find the keyboard is a good second point of access, but sometimes you need to remove the palmrest. Usually once I’m having to do major surgery, I just replace the paste and clean the dust all at once.