To add some table controls to the TinyMCE editor, you will need to change two settings. You can find these under System -> System Settings and choose "tinymce" in the namespace dropdown - that's the one defaulting to "core" on top of the grid.
In there, find and add the following:
- tiny.custom_plugins: Add 'table' somewhere in there, making sure it stays a proper comma delimited list.
- tiny.custom_buttonsN: Any of the 5 settings where you want the table controls to be shown, for example tiny.custom_buttons3, and add 'tablecontrols' while making sure it stays a proper comma delimited list.