Meaning, in which directory? I can’t find this on google, including this site. This thread with these keywords will help lots of newbies. To people who know the answer, does this also apply to any other distros? Please list them in your answer. This q/a will be very helpful to thousands of people.
By default it doesnt do anything … after that it depends on what helper you use.
For example if I am using yay I can set the location in ~/.config/yay/config.json
In pamac its /etc/pamac.conf
If you were doing it manually, or if a tool simply relies on the configuration of makepkg, then its setting is likewise in /etc/makepkg.conf.
PS … this is well documented all over the place … ex:
https://wiki.archlinux.org/index.php/Makepkg#Package_output
I think “thousands of people” needing help should read the wiki(s) 
Note:
As your question was framed within the AUR specifically, I answered according to build directories (where software is compiled).
Others have answered the interpreted question ‘where do the files reside on the system when I install an application?’
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Let me get this straight… You installed something from the AUR and can’t find it.
See the files owned by a package:
pamac list -f <package-name>
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UNIX operating systems don’t follow the volume-oriented approach of Microsoft Windows, and once an application has been installed, it becomes an extension of the operating system. As such, the application’s files will be installed in the directories reserved for that purpose, being /usr/bin, /usr/lib, et al.
Whether the application comes from the AUR or from the main repositories makes no difference in that regard. An exception to the rule is with containerized applications installed via Snap or FlatPak, as well as Steam games and the likes, because by definition, none of that stuff is integrated with the operating system itself, and many (if not most) of the Steam games were actually written for Microsoft Windows.
Also, applications that are installed in a binary form without using the package manager or applications that insist on some special kind of file hierarchy ─ e.g. Discord ─ are usually installed under /opt, and applications installed by compiling from sources by hand usually go under /usr/local.
For more information, see… 
Filesystem Hierarchy Standard
Yes, most distributions abide by the UNIX paradigm ─ there are a few that don’t, like GoboLinux.
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There is no “default” directory, because all packages, the ones from AUR inclusive, all install files in different places according to their needs.
If you want to find out where an AUR package will install the results after the build process, you can inspect the PKGBUILD file of it.
If you want to know which files were installed after you have installed a package, AUR packages inclusive, you can:
Approximately what % are in /usr/bin, /usr/lib, /opt, /usr/local, and the “et al” category? Like, are 90% of apps in /usr/bin, and 90% of AUR compiled apps in /usr/local? This is a near-constant source of aggravation in Linux, but pretty smooth sailing in Windows and MacOS. This question will hopefully help numerous noobs googling after they install something and it doesn’t show up in the System key launcher menu search.
… I wonder how many people have actually looked at the directory structures of macos and windoze …
Theres not a lot to rave about in comparison to unix/linux … but ok.
Besides which … it doesnt matter … we work with packages … you shouldnt need to go snooping around.
For example … where are firefox files?
pacman -Ql firefox
Anyways … its all well defined by standards like the link already shared:
What you, or some app, does and whether it fits those standards may be a different story.
Nothing from the AUR should install there. See:
https://wiki.archlinux.org/index.php/Arch_package_guidelines#Directories