I don't believe the mini is considered to have "User installable" options, so I suspect that you'd have to get an Apple Certified Technician to do it. Otherwide, I'd just google for options on how to do it yourself.
i've just gone through a similar issue, and the only solution would be one of the many usb 'dongles' on the market today. that said, be careful which one you buy. very few (almost none current) offer mac drivers with the package, as mac support is still limited in this field.
there are third party drivers available but you gotta do a little research and digging. the problem seems to be with the number of options of 'chipsets' on the market, and their usage by the wireless manufacturers. if they could stay consistent with one brand of chipset things wouldn't be so complicated, but they seem to switch between chip makers adhoc.
this is what i can suggest to get you going in the right direction:
1) google for the major chip makers and see if they offer mac drivers - atheros; available for cards but not dongles, through 'orangeware'
check out http://atheros.rapla.net for devices
ralink; available for dongles but finicky to set-up
check out http://ralink.rapla.net for devices
broadcom; used by mac but few dongles available
check out http://broadcom.rapla.net for devices
and lastly, be careful when making the purchase, and choose the one with the right hardware version - as i said before, the device makers switch chipsets within a product line, and only change the hardware version number - all else looks the same.
good luck and happy wireless surfing!