I've healed as a Tank healer before cata, in Lich King and before that. I've also leveled a Holy priest. The basic idea is this (for the two new spells)
You use Chakra, then depending on the situation your in: (Lets say, for this exercise, I'm a raid healer and need to get many heals off as fast as I can to my raid.)
I cast Chakra, then use Prayer of Healing. What this does is increase the healing effects of your Area of Effect spells by 10%, and reduces the CD of Circle of Healing by 2 seconds.
With that, you have a new spell called Holy Word: Chastise. EXCEPT! Once you use Chakra, then one of the spells Chakra has on it, it puts you "in the zone" for that specific healing mechanic.
If you use the new Holy Word: Sanctuary, it will drop an AOE circle that heals 466 every 2 seconds for 18 seconds.
See how it's starting to work? The Holy Word has a long CD on the Renew and Heal version. But this one has a short one.
I'll tell you what the rest of the Holy Words do, and small descriptions below them:
Holy Word: Serenity (heal) Instantly heals the target for 7296 and increases the critical effect chance of your healing spells 25% for 6 seconds.
(This is for single target healing. I.E. Tank healer)
Holy Word: Chastise (Nothing/Smite) Chastise the target for 2787 Holy Damage, and disorients them for 3 seconds.
(If nobody is takin' damage, Fire up some hurt!)
Holy Word: Aspire (Renew) Instantly heals the target for 3201 and another 6060 over 18 seconds.
(This is a HOT system, like Druids, you can easily and quickly heal groups, casting renew every .5 seconds. Along with that, this allows you to slap a fat spankin' heal on someone who might be taking a lot of damage, and then have it heal them over time.)
Holy Word: Sanctuary (Prayer of Healing) Blesses the ground with divine light. healing all within it for 466 every 2 seconds for 18 seconds. Only one Sanctuary can be active at a time.
(This allows you to heal MULTIPLE allies grouped up at once. Along with that, the Chakra version of Prayer of Healing allows you to cast it 10% more effectively, with a 2 sec less CD on Circle of Healing.)