I'm trying Manjaro in a VM. I wanted to install Dolphin (the emulator) just to see how you install things in Manjaro, and decided to try to compile it by myself. And I did. I just compiled a program for the first time in my life.
Jokes aside, is this how you're supposed to install software that isn't in the repos in Manjaro? Because it took like 20 minutes to compile lol.
If it isn't in the repos, enable AUR. From a quick search, dolphin-emu should be in the standard repos, dolphin-emu-git has an AUR package. If you use the AUR you'll still be building from source technically, but you'll be using community provided PKGBUILDs which help make the installation process a breeze.
As a general rule though, don't rely on AUR too much, don't use -git versions of software where possible (but for Dolphin, I'd say go for it), and scan through the pkgbuild before installing if you are paranoid since you are dealing with community scripts at that point. The AUR is the biggest source of software you'll ever find, it has everything, but it's also more risky than officially packaged repos.
Most manjaro users use an AUR helper, we can have a discussion if they are a good idea or not another time but I'll just assume that's what you want for now. From memory, you'll either have Pamac (most of the time) or Octopi (KDE) GUI frontends installed already, they are probably the easiest place to start.
In Pamac, it should be as easy as opening the preferences -> AUR -> Enable AUR. Then when you search for dolphin, there will be an AUR tab on the left where you should be able to find dolphin-emu-git.
In Octopi you'll need to first install Trizen, Pacuar, or Yaourt then enable it in Tools -> Options -> AUR. You'll then get a little alien logo in the top panel near the search bar. Click it, then you can search the AUR. Of the 3, I have the best opinion of Trizen, but quite frankly none are ideal.