Turning to the Digital Video Essentials disc, it inevitably has a series of test signals dedicated to getting your contrast right - hardly surprising given its importance in the general video scheme of things.
If you're new to the world of TV calibration, I would recommend (through gritted teeth) that you actually listen to the mostly deathly boring introductory stuff on the disc - all 97 minutes of it - even though it drags on interminably and is far more technical than it needs to be. If you pay attention and ‘skim listen' the techie bits, among all the rambling are a few salient points that should help you better understand what you're going to get up to with the test signals.
If you're reasonably knowledgeable in the field of calibration already, you can take some of the pain out of the DVE introduction by choosing the ‘Setting up my HDTV' programme option from the front menu and pausing the narrative to make your adjustments when instructed. Or, if you really can't hack the spiel at all and have some knowledge of TV calibration test signals, you can thankfully choose to head straight for the test patterns.
The key test patterns for optimising your TV's brightness/contrast balance are the Pluge signal (which helps you optimise brightness), and the reverse grey ramps patterns. With the Pluge signal, what you're trying to achieve is the brightness setting where the outer, blackest bar in the signal blends into the background colour, leaving the two inner vertical stripes looking just visible.
With the Reverse Grey Ramps, you need to push the contrast up until either the dark or bright sections of the video scale ‘clip', meaning that different shades start to blend into each other. If it's the white segments that start blending, before adjusting the contrast again try nudging down the brightness, or if it's the black segments that blend, nudge the brightness up.
Obviously this could have an effect on the results of your Pluge adjustments earlier, and so I'd advise you to keep going between the Pluge and grey ramp patterns until you get what you judge to be the best balance between their demands.