New to Drywalling.
 

Me and my soon to be wife are in the final steps of sanding the seams and corners in our first attempt at using drywall. We are getting ready to start painting over the weekend and was wanting to know how to clean the walls (unpainted in one room and previously painted in the other room) berfore priming? Thanks in advance for your help.

new drywall doesn't need to be cleaned, just primed and painted.
painted surfaces may need some cleaning, sanding or deglossing. If these surfaces have been exposed to airborne grease or candles then you may have to chemically clean them with a mild mix of TSP & water.

In addition to the post above, I would suggest making sure all walls are dust free, particularly unpainted drywall. If there is much dust at all on the wall the primer will not adhere well and the paint can get erasers sized bubbles in it, usually when you apply the next coat. These bubbles will get larger and more numerous when repairs are attempted so it's important to get this step right the first time. Also, use primer on all walls (even old paint) to make sure there is a good bonding surface and since you have no idea whether the old paint is oil base or latex. You can get the primer tinted to closely match your new color which reduces the need for additional coats of paint.
hth, Doug

What is the best way to clean the dust off of the new Drywall panels? I thought about using a damp sponge but I don't want to harm the drywall.

Probably the best way is to just wipe it off the walls with a dry rag, and then vaccuum it off the floor.

Or, just use a leaf blower to make short work of it. :)

It doesn't take a huge amount of effort to clean dust from a wall. Commercial painters just fasten a rag around a broom and "sweep" the wall. Make sure to hit the edges and corners real well. The rag makes sure there are no streaks of dust left behind. Also, a damp (damp, not soaking wet) sponge wouldn't harm drywall but if you do this make sure the wall dries real well first. A wet wall won't hold paint well either.
hth, Doug

Look for something called a "tack rag" made for picking up dust.