My sister wore her engagement ring on the middle finger of her left hand (I believe it's an eastern european/polish tradition? Her husband is polish...).
Claddagh rings (heart w/ crown surrounded by 2 hands) take their meaning from the way they're worn and on what hand: right hand / point of heart facing away from wrist --> looking for love/friendship; right hand / point of heart facing wrist --> in a (committed) relationship; left hand / point of heart facing wrist --> very/permanently committed; left hand / point of heart facing away from wrist is not commonly worn.
The traditional ring finger (on the left hand especially) is historically thought to have a mystical connection to the heart, which is why wedding/engagement rings were commonly worn on it. More important than the finger it was worn on is the circle shape of a ring, symbolizing continuity of love/faithfulness.
Gold is common (for wedding/engagement rings) because it is a precious metal although platinum is also worn by many.
Diamonds are traditional for engagement rings (since 1477), although many people choose different stones now. Symbolic rings such as the claddagh or gimmel rings are also used for weddings/engagements.
But in general? The meaning of the ring is given by the one who wears it, although some are more obviously "married"/"engaged"/"just friends" than others...
~Ladi