During your journey on the Event's islands, you will meet characters that will block your way - Pulsating Anomaly. For interacting with them and in order for them to let you go forward, you will need Magic Dust.
Please note, the Event is a monthly activity, so each month there will be new characters which will block the path and new resources for interacting with these characters. However, this article is being regularly updated. :)
Feed these anomalies and you're good to go ;)
Sometimes you can go short on Magic Dust, so it is important to collect as many of them as possible. Here how you can gain them:
1) Free gift
You can receive a chest via Free gift option once per every 8 hours. Just press on the "Get gifts" icon and choose "Get free" option.
2) from special objects on the islands
On your adventures through the islands of the Event, you will find these special object (Magic Dust). Cut your way through to reach it and you will be rewarded with additional Magic Dust!
Also, you can use the Converter to exchange excessive resources for a set of other ones, though beware, as it is a matter of chance what Dust exactly you will receive ;)
To learn more about the Converter just click on this link. (read it before using the Converter!)
You can also receive the needed resources as gifts from the game's Official Page on Facebook.