Set up Visual Studio Code to be your default difftool by adding this in your ~/.gitconfig file.

[diff]
    tool = vscode
[difftool "vscode"]
    cmd = code --wait --diff $LOCAL $REMOTE
Go to your Git project. Type in:
git difftool {{branch you want to check with}}, for example git difftool master
You will be prompted for each file, if you want to open it in Visual Studio Code or not.
                Is there a way we can see the list of all files to diff in visual studio code instead of opening one by one (like how we see by clicking the git icon on the left side panel of visual studio)?
– Sathya
                Mar 17, 2020 at 16:18
                @Sathya once you are done with settings shared by Boncho     git difftool --dir-diff   should do the work or you can use alias [alias]      df = difftool --dir-diff in your config file
– Mr.Ali
                Nov 17, 2020 at 6:43
                There is also existing a nice visual code plugin 'git-tree-compare' that shows your diff changes to a specific reference branch.  See: marketplace.visualstudio.com/…
– ruuns
                Jan 2, 2021 at 12:22
                as a one-off command, vscode itself can be used to compare two files: code --diff file1.txt file2.txt
– Ryan Norooz
                Nov 2, 2021 at 5:47
Opening up settings (On window/linux File > Preferences > Setting. 
On macOS  Code > Preferences > Settings) 
Search for diff
The specific setting is Diff Editor:Render Side by Side. Mark the checkbox.
                Can you be more specific? How do you "open up settings"? The "gear" icon in the lower left? Something else? Respond by editing your answer, not here in comments.
– Peter Mortensen
                Jan 21, 2020 at 15:06
                If you have a pending update - try restarting visual code after changing this setting. I had one and changing only worked after the update
– StackUnder
                Sep 1, 2020 at 18:44
                @PeterMortensen, almost a year passed, but maybe someone will find it helpful. Anyways, on Windows you press CTRL+P, then > and then type Settings, menu rolls down, and I would look for UI menu option.
– Gabrielius
                Oct 13, 2020 at 13:11
After hours of searching, installing and uninstalling extensions, it seems this is already implemented in VSC.
Just click on the top right icon - "Open changes"
And go back to seeing only the file, not the changes, by clicking on the... top right icon - "Open file"
If you want to compare between two arbitrary references - for example comparing between branch and branch, or a commit and another commit - and still view all files in one shot easily just like we see the index changes.
Install the GitLens extension
Go to the Source control in the left pane.
If you don't have the icon then you can look under menu View -> SCM (Show source control) or use the  defined shortcut.
Expand the last section Search & Compare
Click on button Compare References...
Pick the references, and then you will see the list of changed files and clicking one file will show its changes side to side.
I have answered a similar question here.
But basically you can use the following command:
git difftool -x "code --wait --diff"
    tool = default-difftool
[difftool "default-difftool"]
    cmd = code --wait --diff $LOCAL $REMOTE
Save the changes. Open a terminal in Visual Studio Code by running Ctrl + Shift + `. Run the following command in the terminal:
git difftool master origin/master
Click Git icon on left side of VS Code
If you've made changes to the file(s) since last commit, you'll see the file(s) listed under "CHANGES"
Right click the file name (under "CHANGES") and click "Open Changes"
This will open the two versions of the file side by side with the changes highlighted
You can diff any two files by first right clicking on a file in the EXPLORER or OPEN EDITORS list and selecting Select for Compare and then right-click on the second file to compare with and select Compare with <file_name_you_chose>. 
Alternatively from the keyboard hit Ctrl + Shift + P and select menu File → Compare Active File With... and you will be presented with a list of recent files. Example:
                First, the question clearly asks about git diff in which case there will not be two files, rather only one. Second, you need to install another extension in VS Code, like "compareit" for enabling the option "Select for Compare" and "Compare with Selected".
– KatariaA
                Jul 30, 2019 at 13:19
                @KatariaA: For the second point: It seems to be installed by default (Visual Studio Code 1.41.1 (on Ubuntu 19.10)). Can you confirm?
– Peter Mortensen
                Jan 21, 2020 at 14:48
                @PeterMortensen Yes it's there, no need for an extension: code.visualstudio.com/docs/editor/versioncontrol#_viewing-diffs
– rmcsharry
                Feb 7, 2021 at 20:10
Vscode itself is able to show differences between any two files:
code --diff file1.txt file2.txt
i believe this is independent from git diff feature.
For a quick single file diff view in VSCode without further integrated navigation and edit experience you can configure and use the git difftool as explained by other answers - or more safe (and global) like this:
git config --global difftool.vscode.cmd "code --wait --diff $LOCAL $REMOTE"
git config --global diff.tool vscode   # optionally as default
For a fully integrated experience for such kind of custom diff in VSCode do like this:
# possibly commit or stash a dirty work tree before switching
git switch origin/master --detach  # new master in worktree
git reset master                   # old master as detached HEAD (diff base)
Now you can see and use this "custom diff" as usual in VSCode - as a diff of worktree vs. HEAD : Use the git SCM icon, double/right-click on file changes, toggle inline diff view, etc. .
Now you can even work directly on that worktree right in the diff view. To make a commit of such changes do like:
git reset origin/master    # base for added changes only
# review the bare added delta again (in VSCode)
git add/commit ...
git branch/tag my_master_fixup   # name it
Then merge the new master as usual, switch back to feature branch, possibly cherry-pick the my_master_fixup, rebase or whatever ..
To make this answer work, we must follow a few steps, which, despite having been already repeated in previous answers, I'll rewrite them for sake of completeness.
Open the file ~/.gitconfig, and add the following lines:
[diff]
    tool = default-difftool
[difftool "default-difftool"]
    cmd = code --wait --diff $LOCAL $REMOTE
In some of the answers, the next suggested step is doing git difftool <local_branch> origin/<remote_branch>.
However, there's also another possibility:
git fetch origin <remote_branch>
git difftool FETCH_HEAD
Also, to prevent those annoying prompts from showing up, we can always do:
git config --global difftool.prompt false
On the Explorer panel.
choose a file to compare, then open context menu (right click), then choose Select for Compare.
again, open context menu, then select Open Timeline. Wait for loading previous changes.
On the Timeline tab, you can select a previous version and open the context menu and click Compare with Selected.
Then you will see diff files side by side.
From v1.48 release notes:
As you navigate the Source Control view, pressing Space on a change
will now open it as a preview editor and keep the focus in the Source
Control view, for easier keyboard navigation.
So you could downarrow through your scm file changes and hit Space to open a diff view..  Focus remains in the SCM view so you could keep doing this.
        
Thanks for contributing an answer to Stack Overflow!
Please be sure to answer the question. Provide details and share your research!
But avoid …
Asking for help, clarification, or responding to other answers.
Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.