Depending on whether you have Windows 7, 8.1 or 10, you will have to install the latest updates for your operating system. Without the updates, the game could have a problem with the operating system itself. That is, before installing the updates, you must copy the KB plus the update numbers in case that update might give some kind of problem, because some updates could damage the computer or slow it down (this is only for users using Windows 10).
Once you have the latest updates installed on your system, restart your computer so that they take effect and are solved.

This second step is very important. Without this step, you will have many problems when running the game, in addition to giving you some kind of error.
You must have the latest graphics card drivers installed. You can do this through the AMD or NVIDIA application that you have installed on the computer, whether you are users of any of that type of card. But, through the website.
Once the card's drivers are installed, now you will have to install a series of software that is required to be able to run The Testament of Sherlock Holmes. Many of the games in this franchise use software such as NVIDIA system software and NVIDIA Physx Legacy.
Whatever graphics card you have, you must install it.
The first software is usually integrated when installing NVIDIA graphics card drivers. If so, if the system software does not appear installed on the computer, you can download the latest version from here:
https://www.nvidia.com/en-us/drivers/physx/physx-9-21-0713-driver/
The second software you must install through here since it is quite old software:
https://www.nvidia.com/en-us/drivers/physx/physx-9-13-0604-legacy-driver/

Once you have installed all the drivers for both the graphics card and the required software, you restart the computer once more so that the changes have been applied.

Now, all we have left is to install the game through Steam. Once you have it installed, do not start it yet, because there is still one more step that is also very important because without it, the game would be very unstable.

The game has a rather serious problem in which if we want to save the game both manually and if the game saves it automatically, both the game and the other will crash immediately. This is because the game uses two gigabytes of memory to save the game. So we must install a patch so that the game never crashes us.
The link of the patch I leave it here:
https://ntcore.com/?page_id=371

You only have to download the patch. Once downloaded, you extract it with the winrar or with the program you have to extract files, then run it, when it runs it will tell you which element you want to patch. You go to the game directory, look for the game.exe file of the same game, select it and then click on accept so that the file is patching. Once patched, a window will appear that says "Executable successfully patched".
Close the window and the game will be ready to play. No need to restart the computer again, so you can save yourself this step.

In the forums there are certain people who say they have compatibility problems when it comes to running the game and even playing it. Some say that this game is not optimized in Windows 10, this statement that is totally false since I have played it and I have not had any problem.
However, if any of you have compatibility problems, I will tell you what you have to do.
Enter the game directory, select the game.exe file by right-clicking, then click properties.
Here we go to compatibility. Below we will see the compatibility mode option, check the box "Run this program in compatibility mode for:".
From among all the options to choose, we choose Windows XP Service Pack 3. When doing this, we click on apply so that the change has been applied and then on accepting.
Of course, keep in mind that running the game in compatibility mode will have its advantages and disadvantages:

Advantage; The game can be played perfectly without any problem so that you can enjoy a long experience.
Disadvantages; when you run the game you will not be able to access the steam interface, or take screenshots, or talk to your friends, or anything. Don't worry about the achievement system. Achievements can also be obtained when you are playing.

If this guide has helped you correct all the problems you had with the game, share it with the rest of the community. In this way, they will know the steps they must follow to be able to run the game and enjoy it.
Of all the steps, if you could have any other problem, ask me in the comments and I'll see if I can help you.