What Voltage is the fan? If it is a 12V fan, and I would be surprised if it was not*, then tickling it with 5V from the USB port is not going to do you much good. You can slice up the cable and use the very nice wires inside it to help you but alone it is not going to do much. The fan will hopefully have a label on it saying what Voltage it wants.
Otherwise fans/motors are usually pretty simple -- you will probably have three wires at most and if you are lucky then only two. If it is two wires then one will be positive and one will be negative, for a lot of fan designs it will not blow it up to be connected the wrong way but it will spin the blades the wrong way to get the air flow you want so best to make sure it is what it is. The third wire is then usually a speed sensor of some form so it can throttle it however it will (usually so called pulse width modulation but let us not go there right now). For a normal PC you have 12V capable of supplying more than enough power basically everywhere in the machine, laptops can get slightly more tricky.
*I say having not paid attention to laptop fan electrical specs for a few years now.
Anyway once you have figured out what wire is what then you need to find a suitable voltage source to pull from. Not to mention if you are wiring it to USB it involves slicing some wires and soldering wires (or even twisting them together) where this will probably involve soldering to the motherboard.
If it is 5V then here is a USB pinout
http://pinouts.ru/Slots/usb_pinout.shtml
Assuming your sacrificial cable has the traditional colours then red is positive and black is negative.
If it is 12V then probably better to find someone that knows electronics. It will be trivial for them but above I left out how to find the ground and if that is not something you immediately know how to do then starting on an $800 laptop is not the best plan.
Either way though when you are cutting wires I would make sure you leave enough so you can undo it later if Samsung decide to get it in gear and fix the issue.