My Samsung Galaxy S3 Class A (Korean) was having technical errors, so I reset it. How do I now re-install the OS?
For this you will have to unroot your phone and install stock firmware back in it.
Here is the full process to get it back.
Biggest question still remains: is your phone model the i9300, i9305, SHW-M440S, or something else? This is important so that no errors are made which may lead to your phone become useless. The Samsung Kies software or the Kies Mini software should be the one of most help to you if you want to update/reinstall the operating system firmware. http://www.softpedia.com/get/Internet/Telephony-SMS-GSM/Samsung-Kies-Mini.shtml
You can reset your phone through the default factory option in the Settings section. Well, you may reinstall your phone through the Kies application if you have updated it before (an option for reinstall update is present there.) Else, you have to do it manually and it requires you to root your phone, meaning that you will grant 'administrative' access to the phone and its applications. This will both void your waranty (if still there) and make your phone more vulnerable to malware. So be careful.
In order to root your phone, XDA-Developers is a great place to get all you need. Just go there and search for your phone model (it would be something starting with 'i').
I think you would have done factory reset by going to the steps mentioned in the below article -
How to Hard Reset Galaxy S III
You can restore your OS of you phone by - pressing and holding the Volume DOWN + HOME button + POWER ON button.
If the above steps doesn't help you,then you could try to flash the Samsung firmware of your specific phone model which are SHV-E210K or SHV-E210L or SHV-E210S from the below site -
WARNING :- Be sure to choose only the firmware of your phone only !
You are going to need your exact model number before anyone can really help you much. I suggest going to XDA forums to check out the development section for your phones model number. The section for the international model is http://forum.xda-developers.com/forumdisplay.php?f=1563 This might hold the answers you need.
As for finding the model number go to Settings > About Phone and you can find the Model number listed there. Good luck. If you answer back I will see if I can better direct you.
whether you reset or hard reset the operating system is always inside the phone and will not be deleted.
Hard reset delete all files, parameters...and reinstall the operating system (factory reset)
if you want to update then you can do with samsung kies