1) First ensure that your computer meets the recommended specifications shown below: -
https://www.reallusion.com/iclone/download.html#system-requirements

Note that integrated graphic cards, like Intel(R) HD Graphics are currently not able to support iClone 7/8.

2) If you have already confirmed that your system does meet the requirements, then updating your graphics card driver to the latest one available.
Nvidia: http://www.nvidia.com/Download/Find.aspx?lang=en-us
AMD: http://support.amd.com/en-us/download

3) If you are using a Notebook to run iClone 7/8 then make sure that you run your Independent GPU and VRAM with iClone 7/8, instead of the default Intel Graphics System.

For more information on switchable graphics please check out the link below. This contains additional instructions on how to select the right graphics card option.
http://forum.reallusion.com/Topic212526-386-1.aspx

4) Run Windows Update to ensure that your system is fully updated.
In Windows 7, clicking Start > All Programs > Windows Update > Check for updates.
In Windows 8, go to the Start screen and type Windows Update. Then select "Check for updates" from the search list.
In Windows 10/11, clicking Start button, then select Settings > Update & Security > Windows Update > Check for updates.

5) If you still have problem in Windows 7, please have installed the latest Windows 7 SP1 updates (KB 2670838): -
https://support.microsoft.com/en-us/help/2670838/platform-update-for-windows-7-sp1-and-windows-server-2008-r2-sp1

6) For issues where iClone 7/8 refuses to start but you don't get an "Initialization failed" error, try right-clicking the iClone 7/8 icon and choose "Run as Administrator".