I have a table that is at the very top of a page. I dragged it there and can't move it down. I can't do CRTL+Z to move it down. Every time I put the cursor on the Move Table Handles in the top left hand corner of the table, it automatically goes to the 'double click to hide white space' arrows.
Is there a way to move it.

Two things that might work: they are under Properties in the Layout tab in Table Tools, which should show up in the ribbon if you select the table.

If you don't need text to wrap around the table, choose None under Text Wrapping. This should make the table behave like an inline graphic, part of a paragraph, and you can set space above and so on.

If you do need text to wrap around the table, when you choose Around under Text Wrapping, the Positioning button should no longer be grayed out. You can use it to set the position of the table relative to the page, the margin, etc.