then how can i use fceux on ubuntu mate?
I will go long here as this is the sort of thing some guides assume people know, and I occasionally wanted some people to cover for me.
First check if it is in one of the repositories for it, or its parent or child distributions. Always check these first. Such things are usually pretty up to date, and are built to work with the distro at hand so should work, not to mention are usually good code too where going out onto the internet and hoping your machine does not catch something somewhere along the line... yeah. I know years of Windows will have taught you to ignore the Windows store (of which repositories is something of an equivalent) and similar things as hard as you can, something I can quite get behind there, it is not the case for Linux or unix based operating systems.
Apparently it is available for ubuntu
https://packages.ubuntu.com/disco/fceux
mate has no bearing on anything here really. It is a bit more just another way to have some desktop wallpaper but for the purposes of running programs you can have basically whatever you like as a desktop environment and it won't really matter. Some DEs come with some libraries but you just install those like you would anything else that needs a library (or indeed let the OS sort it out). Indeed saying something after the name is more likely to have people assume it is a version name (Ubuntu likes to name its versions after animals -
https://wiki.ubuntu.com/Releases )
Anyway I don't know what ubuntu uses as a graphical package manager these days but that would be a good start (quick search says Synaptic
https://help.ubuntu.com/community/SynapticHowto but there might be alternatives with shinier UIs-- Linux Mint uses another called mintinstall/software manager).
You could go for the command line/terminal option as well (for debian and ubuntu based things there is the apt-get system
https://help.ubuntu.com/community/AptGet/Howto ). Indeed many guides will use this, and people that know what they want to do will tend to find this quicker than messing with a graphical program. As it is something that could change your system fundamentally you will need to run the program with elevated privileges, which for the most part means you put sudo in front of the command -- it is generally said to be short for superuser do.
If it does not exist in the default repos for the system you can see about finding one with it, or in a related distribution (ubuntu originally came from debian and can usually still use deb installers, and linux mint sprang from ubuntu as well). Sometimes these alternatives might do bleeding edge code where the distro lags a bit, or code the main distribution does not care as much about (you might have had to add some funny things to get it to watch a DVD, this sort of thing).
After that you can see about building it from source (
https://www.howtogeek.com/105413/how-to-compile-and-install-from-source-on-ubuntu/ ), or you can see about downloading an installer from the project itself.
http://www.fceux.com/web/download.html (appears to be an older version here, older than the one ubuntu hosts on the link above).
As for extensions then that is pretty much a windows and DOS affair. If they even exist on other systems it is more of a shortcut for things. Some might still use them for light things or things built around Window's approach to the world but most of the time, especially for something as important as executables, then not so much.
If you did want to run something from the command line (can happen) then ./programname is a good bet, and the equivalent of batch files on Linux is shell scripts (
https://www.javatpoint.com/steps-to-write-and-execute-a-shell-script ). For things like scripting languages then you will need to know what each of those needs as they can vary how they want to be run.