The ring of invisibility is one of the all time classic magic items (D&D, movies, fiction, computer games, you name it).
An invisibility ring is usually a plain band of gold or copper. Putting on the ring makes the wearer become totally invisible.
This is just about the most useful power you could ever have. The spying and theft (you could always just steal from the evil if you have moral qualms about it), applications can quickly make the wearer into a very rich man.
Gaming and fiction has presented us with a lot of different invisibility rings. Not all of them will work exactly the same. Some of them will slowly corrupt the user, eventually turning them to evil. Other rings make the wearer totally silent as well (this is the best kind).
The rings may provide one of three distinct types of invisibility.
The first type is magical invisibility. The wearer cannot be seen, period. You can throw paint on them, and you will still not be able to see them. This type of ring usually stops working if the wearer attacks anyone (or casts a magic spell). Someone wearing one of these rings will not appear to displace any liquids that they come in contact with (like wading in a stream, etc).
The second type is realistic invisibility. Someone wearing one of these is invisible, but their clothes are not (so they must remain nude). You can also spot them by throwing dust, flour, or paint on them. Someone wearing one of these rings will displace liquids normally (which looks really cool, but it gives them away big time).
The Quake style. This ring (known to exist only in the game Quake), would make you become fully invisible for thirty seconds (time possibly adjustable by a server flag). This is not true invisibility, as your eyeballs were still visible. This item would reappear where it was found five minutes after it was used.
Wars have been fought over these rings. You should never ever let anyone know that you have one (or you will end up with assassins knocking on your door late at night).
This is only my interpretation of this item, which is based largely upon its use in the older versions of the Dungeons & Dragons series of games, and in many short stories. Your Ring of Invisibility may be totally different, so always be sure and read the instructions.