The TL-WN725N is a nano USB adapter from TP-Link with 150 Mbps wireless N. In general this WLAN stick is compatible with the Raspberry PI according to the hardware compatibility list. But it depends on the hardware version how easy it is to set it up.
Should work out of the box without any further actions. Just plug the WLAN stick into the Raspberry PI and run the command
to check that the WLAN interface is recognized (normally wlan0).
This version is shipped with the Realtek 8188eu chipset. Driver for this chip are not part of the Raspbian OS. There is a long discussion in the Raspberry PI forum about it. The forum user MrEngman created a driver package for the Raspbian OS. The following steps are necessary to download and install the driver on your Raspberry PI:
wget https://dl.dropboxusercontent.com/u/80256631/8188eu-20130830.tar.gz tar -zxvf 8188eu-20130830.tar.gz sudo install -p -m 644 8188eu.ko /lib/modules/3.6.11+/kernel/drivers/net/wireless sudo insmod /lib/modules/3.6.11+/kernel/drivers/net/wireless/8188eu.ko sudo depmod -a
If everything worked well the command
should list the wlan interface (normally wlan0).
Since the WLAN interface is now available you have to setup the WLAN connection. This is described here.