You can use simple **edit ** 18 - 22 awg wire. Personally, I get mine from Home Depot in the doorbell section. Doorbell wire is perfect for this job.
On the board itself, there are three axis points you can connect to. X, Y and Z. You'll want X which is left and right. There are two solder points (should be labeled on the board) XA and XB. You'll need to connect 4 wires total. +5 volts, ground, -x and +x. As for the +5 power, there should be two points (also labeled on the board) that say +5 and ground. But just in case... ask Randy.
On your Arkanoid spinner, I'm not sure what wires are what. But generally red = +5 and black = ground. The other two wires are not that important. Because if you reverse them, the worst that will happen is the the spinner will go right when you spin left and vice versa. If that happens, simply reverse the XA and XB wires.
Here's a pic of the "no solder version" (not sure which one you bought) which has pins already sticking out. The principle is the same but for the solder version there are no pins present, just solder points.

DeLuSioNaL