I had a bit of trouble first starting out training dungeoneering and wouldn't have been able to understand it without Bizzare's help in-game, btw thank you haha.
1. Click on the quest tab and click on --DUNGEONEERING--
2. Go to you're inventory and a ring will appear
3. Right click the ring and use the teleport
4. It will teleport you to a dungeon walk to the north-east into a gray circular room and click on the "Varrock Portal" in the room.
5. You will be teleported next to a bank stall, be sure to grab any armor that you are not afraid of losing because items will be lost upon dieing while in the dungeon. (A high prayer level and plenty of super restore or prayer pots are recommended for killing the boss)
6. Walk to the south-east and enter the dungeon, have fun dungeoneering ahah:)
I realize this is a simple guide and may not be useful to veteran players but it was kind of confusing for me at first and might be helpful to new players in the future.
