AP and/or pure spell damage will *not* affect your wand damage. You may notice some critical hits here and there with a wand, but that is part of it's weapon damage. There are two things that will increase wand damage:
a.) Putting five points into wand specialization on the discipline section of your talent sheet. This is quite nice for leveling as you will save yourself mana. Less downtime spent drinking.
b.) Putting points into shadow weaving (shadow tree talent) and equipping a shadow damage wand. This increases the target's shadow vulnerability, but don't worry if your wand is not shadow damage. Wands can be fire, frost, nature or shadow damage and while it is nice to have a shadow damage wand to go along with shadow weaving it is more important that you look at a wand for the stats it will give you (usually as you get higher in level you will notice wands with +spirit, ect...low level wands not so much) and also try to get the best dps wand you can afford. There are also many decent wands that are available as quest rewards and thusly free.
*edit*
Just for the sake of clarity, I want to note that shadow weaving will only work in conjunction with shadow damage...in other words, your own or another priest's shadow based spells, a warlock's shadow based spells or in the case of wands...a shadow damage wand.
Edited, Jun 18th 2008 4:20pm by Miskreant