It's not so much that there's a trick to designing a black-and-red site as that there are certain subjects that work well with such a scheme. B/W photography works very well on a black background, for example. Text doesn't.
White text on black is hard on the eyes. Add bright red (for your H1's, say) and you'll glare the user away from the site, eyes watering, reaching for the Tylenol and not very motivated to return. Grey text and dark red on black won't glare but will look gloomy -- great for a vampire fan club website, but probably not much else. :)
The solution is to follow Scott's and DA01's advice, which is the same as mine. Use the logo, but don't let it dominate the page. Make it a graphical accent, an ornament that contrasts with the rest of the site. Your page would be white or preferably a pale grey, with black text. That will make your text much easier to read.
Quite often in design you'll run into situations where you must either match elements exactly or use a bold contrast. In this case, contrast will open up many more design choices and work far better for you than trying to match your logo colors across the whole site.