The Barrows Minigame is located north of Burgh De Rott, and east of Mort'ton. It can be accessed by selecting the Minigames Teleport--->Barrows on the Normal Spellbook, or rubbing the Ring of Duelling (8) and selecting Barrows.
The Duel Arena is located east of Al Kharid. You can get to the Duel Arena by selecting Minigames Teleport--->Duel Arena on the Normal Spellbook, or by rubbing the Ring of Duelling (8) and selecting Duel Arena.
The Pest Control Minigame is located southwest of Ape Atoll. You can access it by selecting Minigames Teleport--->Pest Control on the Normal Spellbook or by rubbing the Ring of Duelling (8) and selecting Pest Control.
There is also a dangerous version of Clan Wars, which could be accessed by the Spellbooks.
Due to an update, this Minigame has been removed by Jayarrowz.
The Puzzle Boxes Minigame can be accessed by selecting City Teleports--->More--->Lumbridge on the Normal Spellbook, and walking north of the Lumbridge Castle. To start the Minigame, you need to speak to Donovan the Family Handyman to obtain a Puzzle Box.
The Soul Wars minigame can be accessed by clicking on Minigame Teleports, selecting "More" option, and than select "Soulwars".