Create lots of ruler guides (too intrusive)
What is wrong with using just 1 horizontal and 1 vertical ruler?
Click on Arrange then Rules guides and choose either Add Horizontal Ruler Guide or Add Vertical Ruler Guide. If you want to remove guide then hold Shft key pressed and drag the guide to the position you want. Now click on tools and then Snaps to Guides. Now the object you dragged near the guide will snap to the grid and will be aligned automatically.
Source Make Alignment a Snap
Can I snap control handles to an arbitrary regular grid in Publisher 2010?
Use "Grid Guides". Make the column and row guides spacing the same. See the link for a complete tutorial.
Source Layout Guides in Publisher- Tutorial and Instructions
Where is snap-to-grid in Publisher 2010?
"Publisher Options" > "Quick Access Toolbar" > Select "Snap to Ruler Marks" > "Add" (to Quick Access Toolbar).
This will place the "Snap to Ruler Marks" feature on the toolbar at the top of your page. It does NOT, however, automatically enable that feature.
You then have to place a tick in the check box to the left of that command to activate it in your document. Only after placing the check mark will the "Snap to..." function work.
Source Where is Snap to Grid in 2010?