With Patch 1.2 you'll be able queue up for dungeon, rift, and quest groups!

On May 10 when Rift's Patch 1.2 goes live the LFG Tool should be available to all Ascended. This new game feature allows players to queue for a specific dungeon, join the random dungeon queue, or look for quest or rift groups. 

Access the LFG tool from the main menu tray in the lower left corner of the screen or press "I".  Select Dungeons, Rifts or Quests from the tabs at the bottom of the LFG tool, then choose from your available roles across the top of the window. When formed, dungeon groups will be automatically teleported to the dungeon, but quest and rift groups will have to make their own way. Join your party and indicate your readiness. You're off!

Additional rewards are granted for completing a random dungeon through the Looking For Group tool - these can be gained up to seven times per week but are not restricted in number per day, so you can do as many or as few as you like each day of the week up to the weekly cap. To qualify for the special rewards you must be ported into the dungeon with your group.

Right now the LFG Tool is single-shard but according to Scott Hartsman that may change in the future.

This guide is also available here in our wiki.