The most serious info first: I’m a native German, so I could do a lot of grammatical mistakes.
I wanted to install the Brother DCP-L2530DW driver, so I have gone to https://aur.archlinux.org/packages/brother-dcpl2530dw/ and downloaded the snapshot from there. In the downloaded Tar.gz I have found only a PKGBUILD file. I haven’t seen such a kind of file in my whole life and I don’t know what to do with this. Have I done anything wrong?
I would be pleased for rather help.
No need to go that route at all. AUR is supported also from our graphical installer. Go to settings and enable AUR. Then simply search for brother-dcpl2530dw and select to install it. Pamac will do the rest.
Or you can open a terminal and issue: pamac build brother-dcpl2530dw
To make the process easier you could use pamac (or the graphical tool: pamac-manager) to build that package.
look into how “makepkg” works …
The Arch wiki is your friend - and even here might be some tutorial on how to use a PKGBUILD file to build a AUR package and install it.