One way to get better control over object placement is to use the arrow keys to nudge the item one pixel at a time. To move an object in this manner, select it and then use the key combination Alt + Arrow, either the left, right, up, or down arrow depending on which way you want to move the item.
This technique works nicely in conjunction with the dragging option. First, drag the object as close as you can to the position you want it to occupy, and then use the Alt + Arrow combination to nudge it the rest of the way into place.
Alternatively, if you want to use the nudge option without relying on the key pad, you can add a floating Nudge toolbar to your screen. From the Arrange menu on Publisher’s main toolbar, select Nudge and then click on the series of dots at the top of the sub menu. (Click on the image below for a larger view.)

click to enlarge
Drag this element to any place on your screen, and the Nudge toolbar will appear.

click to enlarge
You can then nudge your objects by clicking on any of the arrows in this toolbar.