Instructions
Max out Divine Fury in the Holy talent tree and place a point in Chakra in the same tree. Divine Fury reduces the casting time for the Smite, Holy Fire, Heal and Greater Heal spells. You'll often use Smite when leveling up, so reduced casting time will reduce your downtime. Chakra increases the damage of your Holy spells by 15 percent. You can invest points into other talents in the Holy tree to suit your preference.
Place three points into Twin Disciplines in the Discipline tree. (The Discipline tree will only unlock after you have invested 31 points into the Holy tree.) Twin Disciplines steps up your Holy damage spells, such as Smite and Holy Fire.
Open solo fights by casting Holy Fire. Holy Fire deals a lot of damage, but is on a 10-second cooldown, which means that after you cast it, you can't cast it again for 10 seconds. After casting Holy Fire, cast Chakra and immediately spam Smite (cast it over and over again). Smite will be your main damage spell (Chakra is on a 30-second cooldown, which means you can't use it every fight). After you cast Smite two to four times, the target should die.
Join a group by using the Dungeon Finder tool by clicking "Dungeon Finder" along the micro bar at the bottom of the screen. Leveling solo as a holy priest puts you at a disadvantage, because holy priests are geared to excel in group settings. You'll likely gain experience faster by grouping for dungeons than you would by leveling solo. The Dungeon Finder tool automatically groups the necessary classes together, which means you don't have to look for any special group makeup.