My advice would be don't use it. It's a regional word, associated with people from Scotland, Ireland and parts of Northern England. And as you have realised it means 'yes' or is used to show agreement with something. The overwhelming majority of native speakers don't use it because as I said, it's regional. Consequently it would be very strange for a non-native speaker to use it.

It's an outdated word that means 'yes'. Aye is used in Game of Thrones because it takes place in a medieval setting, where 'aye' might have been used.

'Aye' is not really used in common English anymore, so don't worry about using it. It basically means 'yes' but was used in older times, which is why they use it in Game of Thrones. I often hear it still used by Scottish people I believe, but most other English speakers don't use it in regular conversation.

In addition to the above answers, it is used in some settings where voice votes are being taken. This is extremely rare though.

"Aye" means yes. It was originally a Navy term. Sailors would say "Aye, aye, sir" to mean "I understand your order and I will do it." Sometimes in parliamentary voting, people will verbally vote on a bill by saying aye (yes) or nay (no). If there are more ayes than nays, the speaker/chairman will say, "The ayes have it." (more yeses than nos). "Aye" is not normally used by civilians (non-Navy people).