Ah! There's the question.
And - it's worse than that ... Jim!
You quite likely have to connect other "peripherals" to the Arduino as well, each (every) one of which requires a ground connection. (Common trouble brought to these discussions is where external devices such as power supplies have been connected to peripherals but not to the common ground.)
Clearly, you will have to have some arrangement for connecting so many things, which is why there are I/O "shields" offered for the Arduino with banks of pins, or for a temporary experimental arrangement, there are "breadboards" with ground (and Vcc) rails in order to make multiple connections. In a fully permanent design, you would generally solder connections together and/ or lay tracks on a PCB.
In general, you wish to approximate as much to a "tree" (that's the term for which you were looking ;)) or "star" structure rather than a "daisy chain" in order to minimise the length (and thus resistance and inductance) of each path to the main board itself; in practice it usually involves a composite pattern where the connections "daisy chain" along rows of buttons, but the row connections come together at the end of each row.