Centering data within a table cell or cells in Google Docs is straightforward and easy (i.e., highlight and center).
How would I center an entire table?
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 screenshot.
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. Also pay attention to the comment made by
Finally figured it out after spending a lot of time on the problem. Create a table that suits your needs. It will automatically default to the left side. Highlight the entire table by using the left mouse button. Then go up to alignment tab and hit center or left justification. Simply but hard to figure out.
This is not possible in Google Docs at the moment.
A nifty workaround (suggested by Google) is to create a table in your document with three columns. Space the side columns so that the centre column is large enough to contain the table which you wish to have in the centre of your document. Set the border width to 0 (in right click -> table properties) and then insert your table in the centre column of the larger, now invisible table.
For right aligning, do the same as above but make the big table have only two columns, and then space the left column so that you have enough space in the right column to contain your table.