For UI setup, I use Grid and what I call "mouseover" macros. I have one for each heal. This means that I cast on whatever i have my mouse over, usually one of the Grid boxes. The key here is that you don't need to click on and target whatever you want to heal. If you want I can show you how to set this up. There are probably a number of mods that do this or similar. Grid has a few other nice features, like indicating if someone has aggro, which can be useful for anticipating incoming damage.
Probably the toughest part of healing is predicting and anticipating incoming damage. Based on this, you have to make choices about what heals to use, and when to begin casting. Really the best way to improve this is with experience. Practice, practice, practice. Learn from your mistakes. If you have trouble healing a heroic run or raid encounter (and there are some hard ones to solo heal), don't get discouraged, instead analyze where things went wrong, think about what you could have done differently, and try again.
Some practical help I guess: As long as you're not running out of mana, you probably can overheal the tank. Just keep casting your big heal - you can always cancel in the last second. This works in fights where the tank is eating a lot of damage. Reacting with a hot and fast heal sometimes just isn't fast enough. Intense healing fights tend to also be DPS races, not intended to last long. Longer, less healing intensive fights tend to give you more time to use that 5 second rule and let your spirit kick in. You sit back and let your HoTs do their thing while you wait for the next big hit on your tank.
I'm not super familiar with the Priest's group healing abilities, but one thing that I had to learn was when everyone is taking a TON of damage, long cast group heals may not be good enough. I've had to spam instant and quick heals just to keep people up. In that situation, I don't bother trying to top off the group, just keep everyone alive.
Another thing when raid healing is to remember not to fall into a state of tunnel vision. It's really easy to forget to watch for Fire Walls, Void Zones, and any number of other dangers when you're focused on a tank's health. You still have to watch for these things. If you have to move, shield and hot your target as you move, if needed.
Really tho, the best thing is just practice. You have to be able to pick the right spell to cast at any given moment, and knowing which one to use comes from experience. If you have a bad raid, sit down and think about what other spells you could have used, and what the effect would have been. Try out different heals in situations and figure out which ones work best.
Lastly, don't get discouraged. If someone dies because you made a mistake, shove it out of your mind and keep healing. Analyze it after the fight. If everyone takes a lot of damage, don't panic and freeze up. Keep casting heals. Keep everyone up if possible. You have to have a bit of a thick skin too, because some people (not everyone, but some) will blame the healer when the tank or dps dies. If you make a mistake that results in a wipe, apologize and do better the next time. I have found the SGA to be quite forgiving as I learned to heal.
I think that's probably all I can offer without researching the Priest class in more detail. If you have a specific situation that you're not sure how to heal, I can certainly talk with you about it and offer help. Be sure to also check out the Elitist Jerk's forum on Priests here:
http://elitistjerks.com/f77/. There tends to be a lot of math and theory in there, but they know their stuff when it comes to builds and gearing.
Hope that helps!