FTP (File Transfer Protocol) is a way to transfer files wirelessly through a local network. While New 3DS models can do a similar method through microSD Management, said method has a number of downsides:
microSD Management does not exist on Old 3DS models.
microSD Management uses a protocol (SMBv1) that is only supported by Windows.
Additionally, SMBv1 is heavily outdated, now a major security risk , and disabled by default on modern installations of Windows.
microSD Management can cause random file corruption in use.
Luckily, with custom firmware, we can instead use FTP to transfer files wirelessly on both New 3DS and Old 3DS.
What You Need
On your computer :
A working FTP client
Windows: Use WinSCP
macOS: Use Cyberduck
Linux: Nautilus or Dolphin, the file explorers for GNOME and KDE respectively - if not usable, use gFTP instead
On your 3DS :
The latest release of ftpd (any .3dsx or .cia) (Which should come with completing finalizing)
The normal (unlabelled) version has a GUI while the classic version is entirely text-based
Instructions
If your 3DS can use the internet, choose the Universal-Updater method.
Section I - Prep Work
Open Universal-Updater
Tap the magnifying glass icon on the bottom screen, and search for ftpd
Press A on the ftpd entry, and choose one of the four ftpd/ftpd-classic files
Once it finishes downloading, exit Universal-Updater
Did you choose a .cia or a .3dsx version of ftpd?
Open ftpd
Open the Homebrew Launcher
Open ftpd
Section I - Prep Work
Turn the 3DS off
Insert your SD card into your computer
Download one of the four ftpd/ftpd-classic files and move it into the correct place on your SD card
If you chose one of the .cia files, its correct place is the cias folder - create this folder if it does not exist
If you chose one of the .3dsx files, its correct place is the 3ds folder - create this folder if it does not exist
Insert your SD card into your 3DS
Turn the 3DS on
Did you choose a .cia or a .3dsx version of ftpd?
Open FBI and navigate to SD -> cias
Press A while ftpd.cia or ftpd-classic.cia is selected, then select Install and delete CIA(s)
Allow FBI to install the CIA
Exit FBI, then exit the Homebrew Launcher
Ensure your 3DS is connected to the same Internet connection as your computer
Open ftpd
Open the Homebrew Launcher
Open ftpd
Section II - FTP Client
If you haven't already, install the FTP client for your operating system
Open the FTP client and fill in the information as follows:
File protocol: FTP (not SFTP)
Host name/IP address: The IP address displayed on the top screen of the 3DS (e.g. 192.168.0.67)
This is a local IP address, so you don't need to censor it if you need assistance
Port number: The number after the colon in the IP address displayed on the top screen of the 3DS (usually 5000)
If you don't see this option, instead type (ip):(port) into the host name/IP address box, e.g. 192.168.0.67:5000
Username/password: If you see a checkbox for "Anonymous login", then enable it; otherwise, just leave it blank
Click "Login" or "Connect"
If prompted to enter a username or password, press ENTER to leave it blank
Your computer is now connected to your 3DS via FTP!