Red hat based? Install the RPM. Debian based? Install the deb, generally? Install from the repository. You can also install from source if you’d like
You don’t generally download the file like you would an exe or MSI on windows. Rather you enter a command line that tells Linux to connect to the repository (like an app store) of that particular type of Linux, pull the latest installation file and install it.
You can still download the file and install it directly, but it’s not a straightforward double click like on windows.
Look in the OS provided “App Store” first - GUI or not, your choice.
Can’t find what you’re looking for? Look for a TRUSTED alternative App Store source. Then check the App Store again.
Still can’t find it? Look to see if there is a package available that your OS can recognize (different based on what flavor of Linux you’re running)
Still can’t find it? See if you can find the code to build the dang thing yourself.
Installing things on linux is generally the same as phones. There’s a shop-like GUI where you can look up your applications and get them, they’ll also update automatically.
If the software isn’t in your distribution repository, that’s when it starts to be like windows, you need to hunt it down and either get an appimage or something like that, or build and compile it yourself.
