Centering data within a table cell or cells in Google Docs is straightforward and easy (highlight and center).
But how to center an entire table?
This should be easy, but it isn't. I can't for the life of me figure it out.
I just checked and currently it is not possible to do that, on the table itself. There's however a "hack" option available: add a table in a table !!
See example doc I've created: table in a table
If you set the color of the grid lines to be white, than it will fade away. It will also give you flexibility to position the table off-center.
Another hack option which I do sometimes is take a screenshot of the table, paste it into paint, cut off the parts captured in the screenshot not belonging to the table, and then save it as a PNG. I then upload the PNG file to the google doc since it allows for the centering of images.