Message Box has now been released in Cydia so it will be easier for most to just install it directly from Cydia rather than use these instructions.
You need jailbroken device to install MessageBox. You can find instructions on how to jailbreak your device via the iClarified Jailbreak Wizard.
Install iFile and MobileSubstrate from Cydia. Of course, you also need Facebook installed from the App Store.
Click this deb link using Safari on your mobile device.
You will be prompted by Safari to choose an app with which to open the .deb file. Select iFile.
When iFile opens tap the large Installer button.
Once installation has completed successfully, tap the Done button at the top right of the screen.
Reboot your iOS device then launch the Facebook app from your Springboard.
Log into Facebook then tap the button at the top right of the navigation bar to bring your friends list.
Select a friend to chat with from the list and you will notice a chat head appear.
Tap the home button and thanks to MessageBox the chat head will still be present over your Springboard!