System Settings should always be used to uninstall software installed on the console unless specifically stated or you have a reason not to. (Like a broken touchscreen)
This is the process of uninstalling software from your device using one the following:
Open System Settings from the HOME menu
Press Data Management
For installed 3DS software, press Nintendo 3DS, For installed DSiWare, including NDS forwarders, press DSiWare
Software is where all your base software and games are located
Extra data is data created by software to store certain content (Streetpass, Spotpass, etc...)
Downloadable Content is where DLC and updates are located
Find the software you want to uninstall and tap on it, then press Delete
Power on your 3DS while holding START
Press the HOME button
Navigate to Title manager and press A
Select which drive you want to uninstall from and press A
SD Card is where all your installed software, games, updates, and DLC is located
NAND / TWL is where system software and DSiWare is located
Do not uninstall any system titles! This can cause a brick! If you have a problem with a system app not working, then please perform a system update or a Safe Mode update instead!
Find which title you want to uninstall and press A
DSiWare can be found at the bottom of the list
Press A on Manage Title...
Navigate to Uninstall title and press A
Select which option you want to do and press A
Keep ticket & savegame keeps your save and can be used to keep the save after the game is reinstalled
Uninstall everything removes everything related to the game (excluding DLC/updates)
Abort uninstall cancels the uninstall procedure
Unlock write permissions if prompted
Relock write permissions if prompted
FBI has no safety features implemented and should only be used as a last resort, please proceed with caution!
Launch FBI from the HOME menu or from the Homebrew Launcher
Navigate to Titles then press A
Find which title you want to delete then press A
Titles in Green are installed software, games, updates, and DLC
Titles in RED are system software and should NEVER be deleted. If you have a problem with a system app not working, then please perform a system update or a Safe Mode update instead!
Titles in Purple are DSiWare
Select either Delete Title or Delete Title And Ticket
Delete Title deletes just the title and save
Delete Title And Ticket deletes everything related to the title
I accidentally uninstalled a system app, what now?
If your console is able to boot and access System Settings, then follow these steps to update your console.
If your console is unable to boot to the HOME menu or it is crashing at startup, then follow these steps below to update via Safe Mode:
Power off your console
Power on your console while holding L+R+↑+A
Accept the update and follow the prompts
If your console is unable to boot into the HOME menu and cannot boot into Safe Mode, unable to update due to connection errors, tells you that you are already up-to-date when trying a system update, or a system update doesn't help, follow the CTRTransfer guide.