The main method for installing software (after the eShop shuts down in March 2023,) would be 3DS software archive and custom homebrew software, hShop, which has the software 3HS.
This is the hShop icon and banner. If you do not see this on your home screen, it may not be installed. For installing hShop, please follow instructions on opening FBI and installing the 3hs.cia file.
These are important tips, so please read before scrolling past & downloading content.
IMPORTANT NOTE WHEN USING 3HS: Don't close the system while the app is open, the 3DS will freeze on a black screen when you reopen it and you would have to force reboot it. This seems to be a bug and for the time being, completely close out of 3HS when you are closing the lid of your system.
SEARCH TIPS: Before downloading, confirm that the software is the correct type and region. You can check when you are selecting a software. If you are downloading a game, make sure it says Games -> [Region], if it's an update, it should say Updates -> [Region]. You should generally be downloading content under North America.
DOWNLOAD TIPS
While installing software, keep the system near the source of Wi-Fi at all times.
The bottom screen shows download progress.
If the system freezes, force reboot it by holding the power button for 5-6 seconds and turning it back on.
This will not corrupt any software, but you will start downloading from 0%.
The download may freeze for a few seconds, so wait a bit before resorting to a force reboot.
hShop has several folders and categories. Under each of these categories there will be subcategories, which are usually regions such as North America (where games in English would fall), Japan, etc.
After selecting the category and region, you will see a large list. This list can be sorted by different filters. It is sorted by alphabetical order by default. Once you find the content you want to download, press A. To add the software to a queue, press Y. (From the queue you can install all queued software.)
Once you do, a "More about this content" menu will appear. This shows the version and product code along side everything else. To install, press A. To go back, press B.
hShop has a few different search functions:
Normal, search by text with some filters and things
Text, like normal search, but no filters
hShop ID, search by software database ID (technical)
Title ID, search by software Title ID (technical)
Product code, cartridge product code (technical)
Legacy, more complicated version of normal search, but works the same
This is what normal search looks like, you can select what types of content should be included in the search, what regions, and then you would enter your query in the box that says (empty) . Just tap on it.
This keyboard input should pop up. You can type anything, but as an example I just typed animal crossing. Once you finish typing, press OK.
(empty) should now show up with your query (ex. animal crossing.)
Press Submit to load a list of results.
Now, you can select which one you want to install from the list. Remember to check the category to see if it's the right software.
In this case this is an update for Animal Crossing: Happy Home Designer.
Press A once to load the "More about this content" menu, and then press A again to start installing.
FBI is a more complicated software for managing software, but has a cool feature which allows you to use QR codes to download custom software, compared to loading files onto an SD card and installing them. (FBI can do both, though.)