How to enable serial emulation through USB in a STM32F4 Discovery board?
There are two USB connections on the board - the micro USB connector at the top and then the micro A/B connector for the USB On-The-Go support.  The first connector is the programming interface - this connects only to the programmer chip and not to the actual target microcontroller.  There's no way to use this connection as an emulated serial port.  

As for the USB OTG connection I'm less familiar with it but judging by the Wikipedia page on the subject it seems that it's not really meant for that either - USB OTG is focused on acting as a semi-host for peripherals such as thumb drives or bluetooth adapters or something. Just doing a quick Google search yields no serial port emulators and from my assessment of how OTG works my initial reaction is that it won't work.

However, it is perhaps possible that you could configure the OTG device to act as a regular USB device and then code a serial port emulator to reside on the board, but that's a whole development effort on its own.  You're best off attaching a cable like this to the UART pins on the board and interfacing through the UART on the microcontroller that way.