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[DEPRECATED] how to move Steam games between disks
By God, owner of the Universe
THIS GUIDE HAS BECOME UNNECESSARY AS OF JANUARY 2017 because Steam now has a built-in feature to move games from drive to drive. Too bad there's no hide-feature for guides.

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DISCLAIMER: I'm not saying that this method is the best and/or that it works without problems in all cases!

What I am saying is that in the few cases I had so far, this method worked flawlessly: I exited Steam, did the thing, started Steam again - and all was like before, except the games were in a different place. So, while keeping the disclaimer in mind: I suggest you try if you have this need.
 
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TL;DR (too long; didn't read)
  • Properly exit Steam. (Don't just close the window.)

  • Move the game folders from the "common" folder to the "common" folder on the other disk.

  • Move their appmanifest_1234567890.acf files from the parent folder of "common" to the other disk's parent folder of "common". (Find correct ID numbers via https://steamdb.info/).

  • Open the moved appmanifest files in a text editor. If you see one of the very rare absolute paths, adapt them to the new situation and save. (But keep them absolute, to be safe.)

  • Start Steam and play.
Create an additional library folder on the other disk.
In case you don't have an "official" Steam library folder on the other drive yet (Just creating a folder in Windows explorer is not enough - Steam has to know about it!), read on, otherwise skip to the next section.

Go into the Steam client's preferences and select the "DOWNLOADS" section. Click the button labeled "STEAM LIBRARY FOLDERS". In the window that pops up, you can see one entry - the default library folder "steamapps" Steam creates inside its own installation directory. (In case you can see more than one, stop and think about what you're doing / what you want to do!)

Assuming that there's only one, click the button "ADD LIBRARY FOLDER" and create/choose the folder you want on the other drive. Remember that you can't move the folder later (at least not without complications), so make a wise choice.

Then click OK or CLOSE or whatever seems to close+confirm the windows involved, until you're back in the Steam client.
Determine which files you need.
As you know from the TL;DR section, you don't just need to exit Steam and move the folders, you also need to move their corresponding appmanifest......acf files from the parent folder of the one that contains the game folders, so from the parent folder of "common".

There are several ways to determine which files you need. The simplest for less sophisticated users probably is to visit https://steamdb.info/ and enter the game's name. The search results often have several entries, and it can sometimes be unclear which is which, but if you look at your existing appmanifest files too, you should be able to spot the one right answer. Alternatively, if you only have very few games and therefore only few appmanifest files, you can just open all of them with a text editor and look at the game's name inside.

Otherwise, let the computer do the searching for you: In the Explorer window with the appmanifest files, click on the background of the window so that nothing is selected. Then press SHIFT and right-click on the background of the window. This shows the context menu with the additional entry "Open command window here" - click that. Enter this command:

findstr /I "divided" *.acf

This will search through all files with the "acf" extension for a line that contains the text "divided", while ignoring the upper/lower case (because of "/I"). Any lines that fit the criteria will be listed. So, this would find you the correct .acf file for "Deus Ex: Mankind Divided". I guess now you know how this works in general.

Remember which of the appmanifest files you need for the games you want to move.

According to this[gaming.stackexchange.com] post, some games need .ncf files, which supposedly are named with the game's actual name instead of a number code. They need to be moved, too, so remember which of those you will need! I haven't had such cases yet, though. I suspect this is from the earlier days of Steam.

The post also says that some games have .gcf files, which are from Valve's Source engine. Games with those files should better not be touched, so you would have to uninstall/reinstall those games (Half-Life 2 etc.) to get them from one drive to the other.
DO IT!
Now that you have a library folder on that other disk, and you know what files you need in addition to the game folders, it's time to exit the Steam client. You have to make sure that it is not running. Just closing the window is not enough! Make sure you select "exit" from the menu.

Go to the "common" folder on the disk from which you want to move the files, and also open a file explorer window for the "common" folder of the target disk. If you just created the new library folder via Steam's preferences, you may experience that when you visit it now, there is not yet a folder named "common". Just create one! Steam would do that anyway, and it doesn't matter who does it or how. And go in there.

Last chance: MAKE SURE YOU HAVE ENOUGH SPACE on the target drive. You can find out the amount of space it will take by right-clicking on the selected folder (or on one of them if several are selected) and selecting "Properties" from the menu. Be patient while Windows adds up all the files before you use the displayed numbers for your decision.

Now drag&drop the game folders you want to move from the source window to the target window. You can hold the SHIFT key to make it a MOVE process instead of a COPY process. You can also drag the folders with the RIGHT mouse button, which will give you a little menu once you release the button in the target folder, so you can choose what should happen.

In any case: Make sure that the game folders, once copied, do no longer exist on the source disk.

During the copy operation (or later, doesn't matter), go to the parent folder of both "common" folder windows, and MOVE the appmanifest (etc.) files you decided for earlier. It's best to MOVE them right away instead of COPYING, because you can't run into space problems, and they are probably harder to pick out (I mean "select".) than the game folders, so you want to make sure that you don't have to select them again later for deletion.

Once you have moved the appmanifest files, open them in a text editor and look if you can see absolute paths. Those are very rare in those files, but I have had a few such cases, and this is a make-or-break thing you have to take care of!

An absolute path is one that starts e.g. with "C:\" instead of just a folder name. E.g. if you moved games from your Steam installation on your system drive, you might find a text in the appmanifest file that says "C:\Program Files (x86)\Steam\steamapps\common\Dishonored" (Though I assume that Dishonored has no absolute paths.), which you should obviously edit to say "D:\games\clients\Steam\common\Dishonored", assuming that your target drive is "D:" and that the Steam library folder you created there is "\games\clients\Steam\". I wouldn't just change those paths to be relative, while you're at it. That might cause very unexpected problems with the game.

Ok, done with everything?

Well, that's it then! Start Steam. Play. Enjoy the reward of your labor.
In the future, you have to select.
Steam will ask you, every time when you install a game, in which folder (aka on which drive) you want to install the game. At least, this is true once you have overall more than one library folder defined in the Steam preferences.

It's easy to overlook the little dropdown box in the installation dialog. Make sure you decide correctly, so that this whole endeavor (minus library folder creation) won't have to be performed again later.

Steam will remember your last choice, so if you choose "D:", all following games should install there, too. But you will see the dropdown every time, so just take half a second longer and you're fine.