For me? It depends on the level of 'dirty'. For basic dusting I use a vacuum/blower like this one. Pretty sure it can be found a bit cheaper elsewhere with some looking around.
https://www.amazon.com/Metro-Vacuum-MDV-1BA-DataVac-Computer/dp/B00006IAOR
Before that I used a similar small vacuum/blower, it just wasn't a datavac brand. Canned air works fine but prices climbed especially locally and it never seems to last all that long. Either way, vacuum or blower can only do so much. For non critical components like case, panels, fan blades etc I use a microfiber dust cloth (they're lint free). No amount of little air puffs clean completely.
If it's a deep clean like removing all components including the motherboard to clean the motherboard tray etc, I tend to use a microfiber cloth slightly moistened with a little bit of lcd cleaning spray. It doesn't take much, just something to help any loose dust cling to the cloth rather than fly around. For the motherboard or smaller places I use a few qtips moistened with isopropyl alcohol. Just have to be careful, lots of little sharp bits that like to snag the qtips fibers and quickly make them shed. Another once over with a vac/blower works well. Deep cleans are somewhat rare though, maybe once or twice a year. Just basic dusting and cleaning of dust filters in between times.
Items like cpu coolers or radiators where there's lots of fins, the only way to really get in there and clean it pretty good is to remove the cooler and wash it. With the cooler off and disassembled so the fans are removed nothing is left except the metal. A bit of warm water and light detergent like dishsoap, swish it around, rinse under running water.
If water spots or long drying times are a concern using compressed air, an air compressor (so long as the air isn't saturated with condensation), vac/blower or similar can be used. Blow the majority of the remaining water droplets out of it, maybe a bit of isopropyl alcohol to rinse remaining water away (alcohol evaporates rather quickly and displaces moisture) and a quick blow dry with air. Rather than spend an hour or two letting it dry on its own with a little help the cooler should be dry in 15-20min and ready to use.