Linux

Yes. I'm genuinely unsure how it could be any easier. It's just add the repo and install.

But I suppose it's a lot if you don't know what anything means, so I'll try to explain it at a super basic level. Sorry if this is patronising, I can't ascertain your experience level so I have to make an assumption.

The first thing it asks you to do is:

sudo curl -fsSLo /usr/share/keyrings/mullvad-keyring.asc https://repository.mullvad.net/deb/mullvad-keyring.asc

Hm. Okay so I guess before even deciphering the command, you have to know how Linux works. So on Linux, the first word is the name of the application you want to use, and everything afterwards is stuff that you pass along to the application. It's up to the application to program in the behaviour for interpreting the words that come after the first word. So "sudo" is the name of the application you're using, and all that other stuff is stuff you're telling Linux to tell that other application.

Okay, so what is sudo? sudo is short for Super User Do. It's an application that does something (sudo) as the super user (sudo). Super User is like admin on Windows. So it's for when you want to make system level changes or want to override permission limitations. In the past, or at a basic level, you would switch user, make the change, then switch back to your personal user. But with sudo you can borrow the permissions of the super user for the purposes of that one command and everything works smoother that way.

The way you use sudo is you run the application by typing sudo, then you type in a second application and what you want that application to do, then sudo starts that other application and gives it the instructions you asked to be passed on. The second application in this case is curl.

For example, on Windows you might do sudo photoshop open C:\users\winuser\documents\restrictedfile.psd to open a file in Photoshop that the Windows admin decided you aren't allowed to open.

Let's look at the command again.

sudo curl -fsSLo /usr/share/keyrings/mullvad-keyring.asc https://repository.mullvad.net/deb/mullvad-keyring.asc

Sudo is to get super permissions and doesn't actually tell you what the command does. The application that is actually being run in this command is curl. curl goes to a url and sees it. So it basically just means download whatever is at this URL. Here the URL is https://repository.mullvad.net/deb/mullvad-keyring.asc All that other stuff in this command is technically curl specific, so you have to check how curl works to know what it does. But it does follow Linux conventions very closely, therefore a normal Linux user who has never used curl could still guess what it does with 100% accuracy and would probably use it correctly for the first time without checking how to use it. If you want to learn how to use it, you can use the included manual program man, by typing man curl, and as a convention, almost every Linux application will tell you how to use it if you use the -h or --help flags by typing curl -h or curl --help.

In this case, curl takes flags, these are -fsSLo, that's 5 different flags. A flag is like a mode switch for an application, it's specified with adding a hyphen and the trigger word. The hyphen is useful because an application like curl might want a file path /usr/share/keyrings/mullvad-keyring.asc and a URL https://repository.mullvad.net/deb/mullvad-keyring.asc, so by adding the hyphen, the application knows that fsSLO is not part of the file path, but is instead specific instructions you're giving the application. This is a normal convention on Linux, similar to how Windows applications normally program the X button in the corner to close the window.

For curl specifically, by default curl doesn't save the file, it just displays it in the terminal. So the most basic version of the command would be curl https://repository.mullvad.net/deb/mullvad-keyring.asc and nothing else. Let's look at what the flags do.
-f is for fail.
-s is for silent. Both of these just change the behaviour of curl to give you less feedback and information. Mullvad probably chose to do this to make it more beginner friendly, ironically.
-S is for show error. There's a difference between lower and upper case. Show error means that even though curl was asked to be quiet and not show what it's doing, it should still let you know if there's an error.
-L is for location, it's to allow redirects. Mullvad chose to include this option so that the old instructions still work if the URL changes in the future or perhaps if you have a common typo in your command.
-o (output) writes the downloaded file to disk at the specific location. /usr/share/keyrings/mullvad-keyring.asc. The -o flag is the only one in this list that actually matters and changes what the application does. The rest is just there to be beginner friendly, but I think Mullvad made a mistake in including them personally, as I think they add to the confusion instead.

As a standard Linux convention, flags can either be a single hyphen and a letter or two hyphens and a word or a hyphenated sentence. These are conventions and up to the application, but for curl and most applications you'll use, both work. Similarly, curl and most applications let you use a single hyphen and then all your flags in a row, or separate them with spaces and new starting-hyphens. curl -f --silent -S -L --output file.txt https://lemmy.ml for example.

Okay, so hopefully now you can read it a bit better. Let's look at it again.

sudo curl -fsSLo /usr/share/keyrings/mullvad-keyring.asc https://repository.mullvad.net/deb/mullvad-keyring.asc

Wtf is that file and why do you need it in that folder? It's downloading their encryption key to the folder where apt (a different application we haven't encountered yet) looks for encryption keys. You need this for cryptographic verification. It's a safety measure, and more important for security software like Mullvad. It's not mandatory for adding repositories.

So with this command, you borrow the super user's permissions and you download a file and put it in a folder.

Okay, next part.

echo "deb [signed-by=/usr/share/keyrings/mullvad-keyring.asc arch=$( dpkg --print-architecture )] https://repository.mullvad.net/deb/stable $(lsb_release -cs) main" | sudo tee /etc/apt/sources.list.d/mullvad.list

Okay, this one is actually pretty complicated! Similar to above, how they added all those superfluous flags that make curl quieter, this is another case of the mullvad help-article-writers choosing to make the experience of copy/pasting the commands more seamless by sacrificing legibility.

But let's go through it anyway. It'll be a super quick crash course in how to use Linux.

echo "deb [signed-by=/usr/share/keyrings/mullvad-keyring.asc arch=$( dpkg --print-architecture )] https://repository.mullvad.net/deb/stable $(lsb_release -cs) main" | sudo tee /etc/apt/sources.list.d/mullvad.list

Echo is an application that repeats whatever you type at it. If you run echo hi it'll output hi into the terminal. Deb is an application that installs .deb packages. These are like .msi files on Windows. It's specific to Ubuntu and certain other Linux distros. The stuff that follows echo is a command. deb [signed-by=/usr/share/keyrings/mullvad-keyring.asc arch=$( dpkg --print-architecture )] https://repository.mullvad.net/deb/stable $(lsb_release -cs) main, if you run it on its own, it does something. But because you wrote echo first, it's only words that are being printed in the terminal. We'll look at what it's supposed to do in a minute. After that part, comes a pipe |, this is very important, then a second command. sudo tee /etc/apt/sources.list.d/mullvad.list.

Okay, we'll break this down backwards. sudo you already know. It's just an application that starts another application. In this case tee. tee is an application that takes whatever you give it and writes it to a file. It's called tee because it's like a t-split, it both writes to a file and to the terminal at the same time, so you can monitor what's being written. It's specifically designed to be used with a pipe.

Wtf is a pipe? A pipe | is a built in Linux function that let's you take the output from one application and feed it to another. In this case, the stuff you had before the pipe was a echo command. So the output is what you asked echo to echo back to you. deb [signed-by=/usr/share/keyrings/mullvad-keyring.asc arch=$( dpkg --print-architecture )] https://repository.mullvad.net/deb/stable $(lsb_release -cs) main". That means that tee is writing this command (without the echo part in front of it, because that's your command, not the output from an application) into the file located at /etc/apt/sources.list.d/mullvad.list. Tee by default overwrites whatever was already in the file, and in this case, a mode-switch flag wasn't used to ask it to not do that. So if that file already existed (which it doesn't), it would now be deleted and replaced with what you echo'd into it. deb [signed-by=/usr/share/keyrings/mullvad-keyring.asc arch=$( dpkg --print-architecture )] https://repository.mullvad.net/deb/stable $(lsb_release -cs) main".

What is /etc/apt/sources.list.d/mullvad.list? That's a file that belongs to apt. apt is your package manager, we'll loop back to that. The /etc folder is somewhere applications put their files, rather than where the user is supposed to put their files. Having the user's files separately like that helps with knowing which files you care about when it comes to backups and system migrations and things like that. So inside /etc, apt gets it's own folder, and inside that folder it created sources.list.d, and inside that folder, you're now creating a file for mullvad. In this file is the definition of the new repository you're adding.

[Cutting this up to two parts because API limit]