The red ring is located inside the 9th Level Dungeon of the game. To get there from the beginning of the dungeon:

Up 1 screen;
Left 1 screen;
Up 1 screen (must bomb);
Take the passage way (must kill everything in the room, first);
From where you appear go:
Right 2 screens;
Down 1 screen;
Right 1 screen (must bomb);
Up 2 screens (must bomb both times);
Take the passage way (must kill everything in the room, first) and there's your ring!

Don't forget that you need the silver arrows to beat Ganon! A really good gif map of the dungeon is located here:

http://db.gamefaqs.com/console/nes/..._dungeon_09.gif

Good luck!