If you want to do free motion quilting - in other words if you want to be in charge of the direction, then you have to drop the dogs and ideally use a quilting or embroidery foot. (usually a small cirlce or semi circle) although you CAN do this without a foot. (mind your fingers!)
You must remember to put the foot lever down - even if you don't use a foot.
HOWEVER - if you are doing straight line quilting (stitch in the ditch) then dogs up and whatever foot suits your machine....
If you are quiting a very thick piece then you may want to reduce the preasure your foot is exerting down on the dogs (consult your manual to see if your machine does this)
Hope this helps!