No one wants that. This dreaded declaration announces to your party that the heals or dps are now at an end. It's assumed, of course, that you've already used all the tools at your disposal to rectify the situation. What could you have done to keep from landing in this spot?
It all boils down to your style of play, and the main question to ask yourself is "how much time do I spend outside the 5-second rule?"
This chart should give you some idea of what you're looking for in the way of gear, gems, enchants, and consumables. Some priests may have totally different play styles for dps and healing; however, they should also have two sets of gear, each of which can be gemmed / enchanted as needed and food buffs are especially easy to come by. You ARE fishing and cooking, right? RIGHT?
Since we want to get the most bang for our mana-buck, it's a good idea to get familiar with the specifics of each of our spells, both healing and dps. DPS = damage per second; HPS = heal per second; DPM = damage per mana; HPM = heal per mana; HuOOM = heals until out-of-mana.
I don't know about you, but math was never my strong point. I'm fascinated by it, but rather like a sharp knife, it turns in my hand and cuts me before I'm able to use it as a tool. For this reason I rely on a can't-live-without addon called Dr. Damage, available for download at Curse Gaming. This hot little number adds to the Blizzard tooltip, giving you all of the information I listed above. It takes your talents and + healing / + damage into consideration so all we really have to do is mouseover the abilities on our toolbars and get comfy with the information.
Using my lvl 65 Shadow Priest with 350 Int, 218 Spi, 409 +dam - self-buffed only, in dps gear:
Vampiric Touch, costs 400 Mana and takes 1.5 seconds to Cast. Standard dps is 660 shadow damage over 15 seconds. I can see from the Dr.Damage tooltip that my +Damage adds 517.4 for the base, for a total of 1265 damage. Wait - 660 base + 517.4 additional does not equal 1265. Well, I have fully talented Shadow Weaving and Misery, and this additional damage is figured in on an average. See? This is why we don't try math at home, kids. It's just too scary.
While we're talking math, it's important to note that long-cast-time and channeled spells get the most boost from our +damage; instant-cast, direct-damage spells get the least.
Let's switch over to Prin's healing gear set and check out the mana-efficiency of those heals.
Now we're talking 368 Int, 247 Spi, 551 +healing, and 259 MP5 (93 MP5 while casting).
Greater Heal (Rank 6) has a base of 2090-2427. Add my +healing and we get an average of 2861. This little number crits for an average of 4092, which is awesome. My Flash Heal (Rank 8) bases at 931-1078; with +healing it's an average of 1237 and crits for about 1856. But since we're talking about mana efficiency and avoiding the dreaded "OOM," the most important statistics to look for here are HPM & Heal til OOM.
GH6 offers 3.8 points of healing for each point of my mana; I can apply 31,794 points of healing before I'm sidelined. Flash, however, only gives up 3.2 HPM and after 26,774 points of healing, I'm out of the game. If I can time my heals correctly and stay out of the weeds, GH is going to be the better deal. What about Renew? Well, Rank 11 gives a base of 1010 HP over 15 seconds, and actually averages ~1561 HP. HPM caluates out to 3.6, 26,057 until OOM. Because it's a HoT it gets the full benefit from +healing as opposed to Flash, which get's less than half. So, even though you can heal less through Renew before OOM, it's still a more mana-efficient solution than Flash Heal.
Of course, all of this math and theorycrafting is useless unless you're willing to get out there and try it out live. Spend some time with each of the dps styles, offer to heal a lower-level dungeon for leveling guildies, find out where you're comfortable and where you're challenged. Just, for the love of god, don't be stick-whacking anything. You'll make us all look bad.