Also effective is to increase the efficiency of your cooling. Most systems worth their salt will automatically monitor temperatures at which their major components are running, and reduce or increase fan rotational speed to compensate. So, if you reduce the heat generated, the fans won't have to work as hard and thus will be quieter.
Investigate your system's airflow: ideally, cool air should be sucked into it from one end and hot air expelled from the other. Major blockages across the motherboard cause concentrated pockets of hot air, pushing up every components' temperatures. Clear a path by flattening down cables – sandwich bag ties will do the trick – and rearrange PCI cards if you need to.
Another option: isolate the hottest-running component – usually the CPU. Some cases have an exhaust fitted to their side: a tube that sits around the CPU cooler, usually with a fan on the other end, so its heat is drawn away and vented out the side of the case, rather than spread willy-nilly inside. If your case lacks one and you lack the will/money/nerve to mod it, you can achieve a similar effect with cardboard tubing. Just be sure its exit- end points towards a vent, rather than being pressed against a solid surface.
As dust builds up inside your case – and it will – heat dissipation decreases due to all those dead skin cells coating the heatsinks. Give it a clean every couple of months – a compressed air spray or a vacuum cleaner set to blow should do the trick.
Something else to try is replacing the thermal paste on the CPU with something a little fruitier. Thermal paste is the bond between the CPU and its cooler, there to ensure the heat does transfer from one to the other rather than just lurk between them.
Seems like every thermal paste available claims to be a revolution in cooling and similar guff, and it's true that more expensive stuff can make the difference, but it's as much in the application as it is the gunk itself. Too much can cause as much of a problem as too little, as it ends up being a barrier rather than a radiator. You shouldn't put more than a ricegrain- sized blob on there, and you need to whack the cooler onto the chip as soon as possible so you don't end up with air bubbles inside the goo. Definitely don't re-use it – if you have to take the cooler off for any reason, you must replace the thermal paste when you hook it back on.
Once you've cut the main fan noise, you'll notice other annoyances from the system, such as the distracting insectoid chatter of a busy hard drive. The trick here is to reduce the vibrations caused by its spinning platters and clicking heads. Some rubber washers between it and the case can be all it takes, but if you've got a really noisy drive, about £40 buys a full enclosure for it, to effectively block out all its noise (though will often make it run hotter).
As often as not, it's a democracy of cacophony: every component is making its damnable voice heard. Which means you've potentially got a big job on your hands. Equally potentially, you haven't. Again, if perfect, absolute silence isn't your goal, the task is a whole lot easier. A first step worth trying is the BIOS – most motherboards have some sort of fan control option. A fair few boards also have Windows apps to allow fan control from the desktop, which makes life easier.
Whichever of you can set the fans spinning more slowly, whether it's a prescribed 'silent' option or just reactive to system heat. Note that the heat will go up when you drop the RPM; monitor your system with an app such as CPU- cool to check the temperature isn't going through the roof. A system will continue to function even when the processor's running at around 80°C, but the risk of damage, especially to the chip's overall lifespan, rises sharply.