Same as most electronics really
At the least just blow out the dust with some canned air or an oil free compressor from the outside. Best to do it when off and also best to jam a toothpick or something in the fan to stop it spinning -- spin a motor around and you get voltage out of it, proper electronics will handle it (usually by means of a flyback diode) but I so rarely see laptops or consoles with such things.
Do not use a household vacuum cleaner -- you know when you get static shocks from them... now imagine what that does to sensitive electronics.
Disassemble it to get at the air flow/heat path if you want, personally for the Wii in most cases if you clean the fan from the outside it is probably 95% as good as you will get so no great need to go too much further. Disassembly will vary with item but with the wii it is not so bad, for a lot of Nintendo stuff it will tend to be a mix of triwing and philips/cross head screws. You can look up disassembly/repair/mod videos for whatever you might need, most Nintendo gear comes apart pretty easily.
When handling PCBs it is best if you are have a nice static strap but at the very least touch an earthed point before you handle the PCB. Again either jam the fans or disconnect them from the PCB if you are going to see them spin thanks to compressed air or something.