Looks ok assuming those control pins of yours go to the right pins on the 293 so let's see the circuit: do you have grounds?, the 293's EN pin high?, and have you got VCC2?
edit.... also you should have a pullup or pulldown resistor on the switch to make sure its state is well known. (INPUT_PULLUP is easiest way of doing that.)
To post as image you need to "cheat". Attach as you did, post, right click the attachment and save the address. Then edit the post, or do a new one, and use the image icon (next to the chain link) and then use the saved address in there....
Hmmm that looks ok, so maybe there's a discrepancy between the diagram and real life, but I can't tell from those photos.
Have you measured the voltages at the 293? You have 5V on the logic supply and EN, 9V on motor supply, 5V or 0V on the motor controls as expected? You getting 9V and 0V out as expected? Checked the gnd continuity?
I don't currently have instant access to a multimeter so I can't test those things right now. The motor will run very briefly when attached directly to the 9 volt battery. When I connect the Arduino to the computer and 9 volt battery the motor isn't spinning at all.
Well it would appear that my battery must have been almost dead and I'm now very sad that that was my problem. However, I have encountered another problem because the motor won't switch directions when I press the button.
Easiest way to use a switch is to use the internal pullups. Ditch the external resistor, and wire the switch one side to the digital pin, other side to ground. Use INPUT_PULLUP in the pinMode. The logic is reversed since a push is now low whereas before it was high, but that's no biggy.
I think that will be my next purchase! So removing the external resistor helped because pushing the button will now stop the motor but, it doesn't change the direction should something be added to the code?
I did change the code to "pinMode(onSwitch, INPUT_PULLUP)" but it didn't allow the motor to change directions. The wire to ground should be placed in the same place that the resistor was correct?
Also, pressing the button now makes the arduino lights turn off which seems like it is probably shorting out like you said so I'm going to assume I did something wrong.