This is a list of general troubleshooting steps to take when the game does not work, or shows issues while playing. None of these steps guarantee that your specific problem will be fixed, but these actions tend to fix the vast majority of issues.
The steps are listed in order of severity. There is no need to do everything on the list - indeed, some of the last things are far more severe and should only be done if nothing else helps. You will want to check in between each step and see if that fixed the issue, and if so no further actions need to be taken.
Restart the game. This is an obvious first step, but always worth trying.
Restart your computer. This tends to help in some cases.
Verify game files. This helps in case part of the game has gotten damaged or corrupt. If you use the Steam version, right-click the game in your library, choose Properties, go to the Local Files tab and click "Verify Integrity of Game Cache". If you do not use the Steam version, you can do this directly from the game launcher.
Check for Windows Updates. Sometimes issues are caused by Windows and running Windows Update may help - this is especially true after major Windows patches which may have follow-up updates. Check this article for instructions on how to check for Windows updates.
Update your DirectX version. Download this (large orange button) and run it. This may help graphics-related issues.
Delete the game config file. For instructions on how to do this, click here. This will reset your in-game settings, but nothing else will be lost.
Reinstall the game. Like the above, this will reset your in-game settings but you will not lose any character progress. You can uninstall the game through the Windows control panel, then install it again - either here or on Steam if you use that.
Reinstall/update your GPU drivers. This tends to fix graphical glitches, crashing, or the game not starting. This is not strictly related to V&H, and will affect all games and GPU-reliant software on your computer. That said, usually for the better! Instructions for how to do this can be found here.
In addition to this list, please see this thread for notes on framerate and graphics settings.
The first step is to open the Device Manager to determine whether you are using an Intel, AMD or nVidia graphics card. How you do this vary depending on your operating system. If you already know what GPU you have, you can skip this step.
Right-click My Computer, click Properties, click the Hardware tab, and then click Device Manager.
Windows Vista and newer
Open the start menu, type in "Device Manager" and open the first entry in the list.
Once the Device Manager is open, click the plus or > symbol next to "Display Adapters". Now note the name of the item that appears below.
If it contains "NVIDIA" or "GeForce", you are using an nVidia card.
If it contains "AMD", "ATI" or "Radeon", you are using an AMD card.
If it contains "Intel", "GMA", "Extreme Graphics" or "HD Graphics", you are using an integrated Intel card.
Download the drivers
Now you can download the most recent drivers for your particular card.