Items for summoning and dispelling anomalies can be found in the Mysticism section of the Store and Inventory.
To summon an anomaly, press the Use button next to the corresponding item in the Inventory. The summoned anomaly will then appear in a random location.
To banish an anomaly, use the corresponding item in a location or mini-game entrance window.
You can also get these items as a reward for assembling collections and completing mini-events.