Menno said:
What you need is a "low profile" PCI wireless adapter. Google it.
But the USB idea is a lot better.
In this picture, the PCI card printed circuit board is low profile.
The metal faceplate fastened to it, is "full sized" or regular
profile. Notice how much taller the faceplate is, than the printed circuit board (PCB).
http://images17.newegg.com/is/image/newegg/33-166-051-Z05?$S640W$
Also included in the package, is a "low profile faceplate". You
unscrew the regular height faceplate, then install the low profile
faceplate. Then, install the (now completely) low profile product
in the slim computer. Next, screw on the antenna (one or more
antennas, depending on the wifi standard you're using). Since that
example product is 802.11n, it has three antennas. Other wifi
cards might have one antenna.
When purchasing low profile products, you have to be very careful.
Some products have a low profile PCB, but the faceplate is regular
height (and useless to someone with a slim PC). In such a case,
the user may have to scramble around, trying to find a different
metal faceplate to screw onto the card. Some desperate people,
modify the existing metal faceplate, until it fits the computer
case. (Pounding, bending, drilling, grinding...)
So when you're shopping, make sure that not only is the PCB
material low profile, but that a low profile faceplate is
also included.
The faceplate is also part of securing the card in its electrical
slot. It may be tempting to just remove the faceplate and operate
the card without mechanical support. If you do so, you're asking
for trouble. If the card hops up out of the slot, the PCI bus
could be damaged.
*******
USB Wifi devices are also available, but read the customer reviews
before buying one.
Paul