Tables are used to display information, not for layout. The table tools in the Web Editor are similar to those in a word processor. The left side of the lower section of the tool bar holds the table buttons:
These buttons can be hovered over in the editor for the following descriptions
Edit row properties
Edit cell properties
Insert row before
Insert row after
Insert column before
Insert column after
If the table is selected, Insert table can also edit the table properties. Tables are best built in the editor, not copy/pasted in. It is wise to save often when working with tables in the editor.
Because of how tables are built in HTML there is not a "column properties" button. Instead use the "cell properties" button to define the cells in the column.