Some of the methods floating around the internet for this black screen issue include smacking the phone against a hard surface (not recommended), pressing hard around the camera lens or giving the entire device a gentle twist. In previous One devices, the issue seems to have been that the internal cable connector was folded and the compression of the fold would cause the device's screen to go black. Some of these fixes worked, some didn't, and most were temporary at best.
The long story short is that this is not a simple issue to fix, but the following steps should help you have the best chance of sorting it out. First thing's first, try a Factory Reset. If your screen never comes on, just watch a YouTube video of the procedure and follow the number of button presses. To do this, go to the Hboot menu by turning your device off and pressing Volume Down and Power until the Hboot menu appears. From here you can access Fastboot/Recovery and clear caches etc, but the option most likely to make a difference is a Factory Reset. Before doing this though, make sure you have done a full backup of everything you want to keep on your device.
If this doesn't solve your problem (it sometimes takes a while to resurface), the next step is to reinstall the latest firmware. Sometimes bugs creep in with firmware updates and cause all kinds of havoc. Doing a factory reset and clearing caches after an update usually fixes any software issues, but you can always do it again just to rule out any problem that may have occurred during the last update process. Again, back up your data before reinstalling the most current firmware for your device.
If you want to do a full reset and restore of your firmware you'll need to run RUU (ROM Update Utility). If you want to downgrade to a previous firmware build though, you'll need to have S-Off (Security-Off) first. That's a whole different bag of bolts though, so I'll have to write a separate tutorial for that. But if you already have S-Off or want to update your existing firmware then all you need to do is head to a reliable repository of RUU downloads like HTC1Guru and flash the RUU exe you want.
If even a firmware replacement doesn't work the next step is to you might want to ensure it isn't a hardware problem, which in many cases, especially with the HTC One X, it is. If your device is still under warranty you should take it to your retail store or service center and let them deal with it. Be advised though, that they will most likely simply do the steps outlined above.
Have you suffered the black screen of death? How did you manage to fix it?