To access the dungeons in Xelorium you have to get to the positions where the NPC who grants access to the dungeons are. This map will show you the way to the dungeons from the starting position when you first enter Xelorium. If you need help navigating the Xelorium, please visit this article.
The dungeons are, from lowest to highest in difficulty (and on the picture):
To access these dungeons, bunch of keys isn't enough. Therefore, you need to craft keys. The recipies for each key to each dungeon are these:
Eye of Vortex
If you want to know more about the dungeons before heading out there, please visit our articles on each dungeon (links to these are just under the map in this article, just click the name of the dungeon you want to know more about).