Access the Planar Attunement Window by either pressing "U" or the Planar Attunement button on the game menu.
Upon reaching level 50 you will receive a letter from Cyril Kalmar or Asha Catari. This is an invitation to attend your Ceremony of Attunement. Completion of the ceremony awards you 200 Planar Attunement Points to get you started.
The cost of each advancement is the large number at the top of the hex, while the rank is displayed in the tooltip and the bottom of active hexes. Once a tier is fully complete, meaning all advancements are purchased at max rank, it will unlock the second tier in that plane.
Greyed-out Attunements are locked. Like the soul tree, players unlock Attunements as they spend points. Players will still be able to see the costs of any attunement on mouseover.
With Patch 1.6.1 Hotfix #7 you can respec your Planar Attunements. Visit your calling trainer in Sanctum or Meridian to initiate a re-spec. The first one is free, but you'll have to pay 100 Platinum for additional later re-specs.
Each planar element gives minor bonuses to abilities and either spellpower or attack power, with various types of weapons receiving the bonus. They also each give a small amount of dps increase vs planar beings of that element, and a resistance bonus to that element. So Earth Attunement gives earth resistance and greater dps vs earth invaders, and so on for the other elements. They're color coded:
For more information about the Planar Attunement trees by class, see these guides: