Depends on what you're trying to save. If you insert a card, the stock camera app will automatically try to save pictures to it (it will ask you first, though...and I strongly recommend against it... you should only use the SD card for disposable data and data you've backed up elsewhere...). Multimedia apps like Spotify or Netflix will also offer the option to use the SD Card for offline data once it's been detected.
If you want to save downloaded files from a browser, most don't support setting up a default folder for it and will save to internal memory.
Some apps will not allow any data saves to external storage.
Again, depends on the app you're using. Just remember, Android places restrictions on apps' access to SD Card files (which is why many just opted out from saving data to them). Any non-stock app can only write/modify files in a folder the same app created. So a photo editing app can open a picture created by the camera app, but will not be able to modify the file or write to the same folder to save a copy...it will have to create a separate folder and then be able to manipulate the files only in that folder.
Apps will also vary depending on the dev (some can be moved, some will only allow external downloads to be moved, some will only allow save files, some will not allow SD card move at all...again, up to each app developer). Once you move apps to the SD card, however, should the SD card become corrupted or unavailable, the app will fail and most likely will need to be re-installed and data be lost if it wasn't backed up.
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