I got the MakerShed Ultimate Microcontroller Pack and it came with a "Transistor NPN". I want to use it (or probably buy something else) as an electronically controlled switch so that on arduino I set a digital output to "HIGH" and it allows 12 volts though or set the pin to "LOW" so that it turns the 12 volts off. This is much harder to explain than it was in my head. Anyway, is that possible? Or do I need a bigger, better, transistor or some other special purpose circuit for this?
Saying you have a "Transistor" is like saying you have a "vehicle", and you're asking us what your vehicle's towing capacity is.
Basically, there are many, many, many thousands of varieties of transistors.
This particular transistor is rated for a maximum (collector-emitter) voltage of 20V, and a maximum current of 500 mA.
This means that you can switch a (small) 12V device with the transistors you have. However, if the item you're switching needs more then 500 mA, you're going to either need a bigger transistor, a relay, or some other switching device.
If you can give us more information on what device you're hoping to switch, we can probably help you determine if the NPN devices you have will work, or if not, what devices/relay/whatever you should use.
As the (oh so fuzzy) datasheet on that site says, the (SS9013) transistor can withstand 20V across C-E and 500mA total. As long as you don't exceed those you should be fine.