In order to get the Edimax USB WLAN Adapter working on Debian / Raspbian, proceed as follows.
(1) Use lsusb to list all USB devices:
$ lsusb
Bus 001 Device 004: ID 7392:7811 Edimax Technology Co., Ltd EW-7811Un 802.11n Wireless Adapter [Realtek RTL8188CUS]
The Edimax USB WLAN Adapter uses the Realtek RTL8188CUS chipset.
(2) To figure out which driver is used and hence which module needs to be loaded, we can use the system message log:
$ dmesg | grep rtl
[ 16.919884] usbcore: registered new interface driver rtl8192cu
Now we know the module name: 8192cu
(3) To load the module during system boot, create the following file with the given content:
$ sudo touch /etc/modprobe.d/8192cu.conf
$ sudo echo "options 8192cu rtw_power_mgnt=0 rtw_enusbss=0" > /etc/modprobe.d/8192cu.conf
(4) Enable the wlan0 device (eth0 will be disabled with this configuration):
#auto eth0
#iface eth0 inet dhcp
auto wlan0
iface wlan0 inet dhcp
wpa-ap-scan 1
wpa-scan-ssid 1
wpa-ssid "your-ssid"
wpa-psk "your-wlan-passphrase"
(5) Reboot your PI