The easiest way to connect LCD modules to Dragon is to solder a female connector (blue on the picture below).
Then most LCD modules plug right in. You may need to solder a male connector on your LCD module, if it isn't fitted yet.
Seen here after power-up but before initializing the FPGA (power is provided by the USB cable).
Then, configure the Spartan-II, send a few bytes through USB (C code provided), and voila!
You can use a male connector and a flat cable.
Note: there are 2 ways to solder the connector on the LCD module, facing down or facing up.
Use the same on the Dragon, facing down or facing up - or the connections through the flat cable will be inverted.