Blow the dust out with compressed air OUTSIDE the building.
Word for the wise: place a soda straw or similar object between the cooling fan blades in a manner to prevent them turning, as blowing the fan with compressed air may cause the motor(s) to generate voltage and feed it back into the motherboard ...
lifehacks.stackexchange.com/users/7840/Kevin_Kinsey
When sitting at my desk today I emptied an 1.5l plastic bottle, and by accident squeezed it a little and let go.
This created a small, but efficient vacuum, which can be used to suck up dust and small debris.
Went to find some dust, and the following does actually work:
Squeeze the 1.5l plastic bottle Move the end close to the dust at a slight angle Release the squeeze, and as the bottle goes back to the original shape it sucks up the dust Repeat operation, but be careful when squeezing it not to blow out the dust again :-)
When executed properly it has the suction to vacuum a few peanuts!
Will the computer be thoroughly cleaned?
Maybe not, but you'll get most of the dust away, and the rest could be wiped away with some non-static cloth.
lifehacks.stackexchange.com/users/4490/holroy
Another good method is to use various sizes of soft bristle paintbrushes, dependent on where you want to clean.
Once the case is opened, tilt the computer at an angle holding securely in one hand, and gently brush downwards in the areas you would like to clean with the other hand.
You will find clumps of dust will drop out easily, especially in areas such as the fan, and the soft bristles of the brush won't damage anything inside.
lifehacks.stackexchange.com/users/7973/Craig Garrity
Go outside the building and use a fan to blow the dust away.
Of course, don't make the fan too strong or this might just backfire on your computer...
Use a portable fan, which are nice and small with sufficient energy but not too strong.
You could also try making your own little vacuum by using suction.
Use a handkerchief, put it over your mouth and suck the air in.
This will suck the dust in similar to a vacuum.
As a matter of fact, this was the inspiration for the first ever vacuum!
lifehacks.stackexchange.com/users/2475/Anthony Pham
A hair dryer on the cold setting will do the job
nicely and good quality ones will even allow you to adjust the strength of the air flow.
Yes, they might not be as precise as compressed air but way more cost effective than buying cans of air and a lot safer than vacuuming in small parts.
lifehacks.stackexchange.com/users/12132/Stephie
Compressed air is perfect, but I have spent one can just cleaning one PC thoroughly.
Now I use a dust remover for SLR cameras (you can buy one cheaply in any store that sells such cameras), and it works for all heatsinks etc.
It doesn't have enough pressure to do it from 15cm, but that's never an issue.
I only use compressed air for keyboards now.
Never use a vacuum cleaner unless you can be absolutely sure you don't touch components.
The metal tube may accumulate and hold significant static charge frommoving air and dirt/dust.
Always turn off the PC by switching the PSU off, or remove the mains cable.
Then discharge the system by pressing the power-on button once.
Never use 'brushes' or anything capable of generating an electrostatic charge.
That charge will find somewhere to live, and it loves RAM and similarly delicate chips.
lifehacks.stackexchange.com/users/21104/user2497
Say I open a desktop computer case and it's very dusty -- not an uncommon situation. However, Oh no! I forgot my vacuum! What else can I use to thoroughly clean the inside of the computer?

I considered compressed air as this is available in most offices, but simply blowing the dust in all directions will mess up my clothes and/or the person's office, so that is not an option.
How to clean the inside of a desktop computer without a vacuum
lifehacks.stackexchange.com
<cleaning><substitute-tool><technology><dust>
lifehacks.stackexchange.com/questions/7909
lifehacks.stackexchange.com/users/15/Mooseman
To clean the inside of a computer without a vacuum cleaner, you could take the unit outside and blow it with either compressed air or a fan. You could also consider using a brush to clean away the dust, however, some people advise against this as it can create static charge. The options are to go outside and blow with compressed air (blocking the fan blades first), squash a plastic bottle to create a vacuum and suck the dust out, blow with a fan or suck through a handkerchief. 
Go outside to blow with compressed air, but block fan blades first. Use a plastic bottle to create suction and vacuum that way. Clean with soft-bristle paintbrushes. Use a fan outdoors to blow the dust away or suck it up with a handkerchief over your mouth. Use a can of compressed air - not a brush as it may generate harmful static.