Red orb cache has no actual visual appearance, but they are located in the most unusual places, usually, where the player would not normally go during the gameplay.
There is no real way to indicate where the caches are located, only to comb the room entirely. However in Devil May Cry 4, Nero is able to detect the Red Orb cache by the blue glow on its "right hand". The glow gets brighter, the closer you are to the cache.
To reveal the Red Orb Cache, the player must stand for a few seconds in the spot where the cache is located. Then a high amount or Red Orbs will flow out of this spot.
In the first and third game, Red Orb caches can only been taken once but in Devil May Cry 4, they will always reappear if the mission is replayed and will remain on another mission if location is still available.