First and most important, the aperture of the lens will determine DOF. The wider open the lens is (e.g. the smaller the f-number is), the more shallow DOF will be. The more you can "stop down" the lense (e.g. the larger you can get the f-number), the sharper the depth of your image will be.

Second, the zoom factor will influence DOF too. The further you zoom in, the more shallow DOF will be. If you want to have large DOF (e.g. most of the picture is sharp, from the front to the far distance), make sure to use a small aperture (large f-number) and zoom out towards wide angle.

Shallow DOF is a great means to isolate subjects from their background (good for portraits) but for landscape shots, you want to have deeper DOF.

Of course this also depends on the amount of light available. The only hint I can give you here is to experiment - and don't be afraid to use high ISO numbers if that's what it takes to get a shot the way you want.

(nubui)