Not all models of galaxy s3 support update to 4.3 jelly bean at this moment. This update is model, carrier & location specific. You can google about it.
Having update through
OTA is the best choice as you always shall receive legal update
(stock firmware) through it. If
OTA fails to receive the update you should understand that either your device model or carrier isn't supporting the update legally.
Samsung Kies also plays role as legal update booster which you are unable to receive through
OTA. If you are unable to receive the update via
Samsung Kies you can be sure that there is no legal update of stock firmware available for your device.
If you are still eager to update your device to 4.3.2 jelly bean, flashing the
ROM is the onliest choice. You can download the
custom firmware of android 4.3.2 jelly bean either
location+carrier specific (download only location specific firmware) and flash it through `ODIN. You shall do that at your own risk. You of course shall backup your device before you do that as you may encounter some incompatibility issues after you flash the custom firmware.
For most of the android versions, you must have your device rooted in order to flash custom firmware. There are many operating system specific resources available on the net about how to root your device.
You can learn more about
ClockworkMod (CWM) recovery &
TeamWin Recovery Project (TWRP) before you root your device.
Anyway, don't forget to install the root keeping app like
Root Keeper and super user app like
SuperSu after you root your device in order to manage your
rooted android as well as keep