Lots of good feedback above. The most important thing to take away from Fontaiine's (sp?) layout is this: the health bars displayed by your raid frames ought to be front and center, so that you can easily keep an eye on both those bars AND what's happening under your own feet. Especially if you have a large monitor - I have a 24" monitor and if I park things too far off to the side, moving my eyes over there means I no longer have a simultaneous view of my own toon's situation.
Once you get a layout you think might work (and copy other people's until you have one - z-perl, all of them let you move your frames around pretty much)... recommend two things to help you learn to watch bars AND be aware of what's going on under your feet. Do lots of LFR, even if you don't need the loot anymore, for the practice, and honor the mechanics even if they won't kill you in LFR because it's good practice to get used to moving yourself while also healing others. You will also have to heal a whole ton of stupid in LFR, also good practice. Secondly, do some random BGs, because the unpredictability of other players will force you to keep track of what's happening to your toon as you simultaneously heal others. Both are good training for healers.
As noted by others, raid encounters are scripted, and as you "learn" each fight, you will eventually get to the point where you know when to pop what spell to gain the most benefit from it. PvP is by it's nature far more random. Spending time at both will help you become a better, faster-thinking healer.