[jquery] How can I get the corresponding table header (th) from a table cell (td)?

That's simple, if you reference them by index. If you want to hide the first column, you would:

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$('#thetable tr').find('td:nth-child(1),th:nth-child(1)').toggle();

The reason I first selected all table rows and then both td's and th's that were the n'th child is so that we wouldn't have to select the table and all table rows twice. This improves script execution speed. Keep in mind, nth-child() is 1 based, not 0.