I don't claim to be a "good priest". I don't even claim to be a MEDIOCRE one. My only priest is currently level 26, and I've only started getting into group play and healing others over soloing my way through things.
That having been said... if you're an absolute newbie to the Priest class, you may find that the early levels of Priesthood (especially) are without substantial power, and therefore soloing your way through quests to get your toon to 20 or so and where you have a handful of instances you can choose to go into is kind of tough.
Lowbie Priest, 1-5
The first secret of lowbie Priest advancement is no real secret at all: Smite, Power Word: Shield, smite, smite. You've got to get to level 5 before you can use the very powerful second secret of lowbie Priest advancement: Procuring a wand.
About Wands
At level five you can equip a Lesser Magic Wand
Binds when equipped
RangeWand
12 - 22 Arcane DamageSpeed 1.50
(11.3 damage per second)
Requires Level 5
Item display is courtesy world of warcraft.allakhazam.com. ',VAUTO,HAUTO,FULLHTML);" onmouseout="return nd();">Lesser Magic Wand, which is created by an Enchanter at a very very low enchanting level. Most times they'll be available for purchase in the Auction House for under 25s, but if you've got an Enchanter toon or Enchanter friend in your guild, you might be able to purchase the materials more cheaply and have your wand fabricated especially for you.
Make no mistake, wands are amazing for a low level Priest or Warlock, or even for a Mage who runs out of mana during fights on occasion. The first time I used a wand I was shocked and excited by how much more quickly my wee Priest's targets went down.
How To Equip A Wand
Equipping a wand for use in battle is done by dragging the wand into your 'ranged' slot. If you have your Character/equipment view up and begin the process of dragging the wand, the correct weapon slot will highlight blue to guide you along.
How To Shoot A Wand
Short version of how to shoot a wand: Drag the 'shoot' skill from your Spellbook ('p' on your keyboard) into your Action Bar, in slot #1, replacing 'attack'. Then, hit '1%26#8242; when targetting an enemy and your wand will start to shoot and will continue shooting until you hit '1%26#8242; again, or until you or the target is dead.
Since you don't start out with a wand, the 'shoot' skill is not on your default Action Bar. Personally, I tend to replace the 'attack' skill in slot 1 with the 'shoot' skill from my Spellbook once I get a wand, because let's face it - my Priest should never purposely be close enough to a hostile mob to whack him with a weapon. Optimally, I'm far away from my aggressors because cloth armor doesn't protect very well.
Sample Fights
My fights tend to look like this:
Level 1-5: Smite, smite, smite, occasional use of staff to melee when out of mana.
Level 5-15: Smite, Shadow Word: Pain, Power Word: Shield, Wand to death.
Before fighting, I will make sure I've buffed myself with Power Word: Fortitude, Inner Fire (level 12) and because I'm undead, Touch of Weakness (level 10).
Spending Talent Points, Level 10-23
If you are going to be soloing with your Priest at all, the first 10 points should generally go into Wand Specialization under Discipline, and Spirit Tap under Shadow.
Wand Specialization because you're going to be using a wand to do most of your damage at low levels.
Spirit Tap because it reduces downtime in recovering mana after killing a mob.
After spending those points, if you're soloing a LOT, you might want to consider putting 3 points into improving your Power Word: Shield.
Equipping Your Priest, Important Priest Stats
Finally, the topic on equipment for your wee Priest.
As with most wee toons, there's not a lot of point in spending a lot of money equipping a regular toon under level 30 - the quests you complete are designed to help improve your equipment over time, and any piece of equipment you pick up will easily be replaced within a few levels if you keep your eyes open.
At low levels, most toons are very weak. Most can't take on more than one opponent at a time without dying. Expect this for the first while and you'll be less likely to spend a load of cash on equipment that only improves your survival chances a small percentage anyway.
Your main stats for solo play at a low level are Stamina, Intelligence and Spirit. Stamina because it raises your hit points, Intelligence because it raises your spell points (mana), and Spirit because it helps you recharge your hit points and spell points more quickly in general.
As your use of mana increases, you might want to move away from +stamina and focus more on +intelligence and +spell damage (+holy or +shadow would be best, as opposed to +frost, +fire or +arcane which are Mage stats).
And of course, always keep an eye out for +healing gear for those occasions you do decide to group up and take on an instance. As a Priest you'll likely have two complete sets of gear - one for solo play that focusses on dealing damage, and one for group play that focusses on healing. But we'll leave that for another entry as I don't think it makes a big deal under level 20 :)