So your iPhone is stuck with a white Apple logo stuck on a black background. You've searched the Internet and somehow ended up here...
I've found that if you try the following you can get it restart again ok:
1) Put the device into restore mode
2) Hold down the power button till it reboots
3) Once it starts rebooting try clicking the power button and/or home button for a few seconds at a time
4) It either restarts normally, or try again - go back to step 1/2
I know it seems a bit random but it can work if nothing else does. Though it probably indicates there's a hardware problem with your device if this keeps happening even after you do a full restore or two...
Update (Oct22): If you're seeing a black screen on a newer iPhone (e.g. 10+ onwards) with only three buttons (i.e. power, volume up and down) then you can try the hard reset sequence:
1) Tap on volume up
2) Tap on volume down
3) Hold down on the power button until it reboots
