CrossRoads:
How fast do you want to turn it On and Off? For occasional switching, a relay control will do.
For highspeed switching, like for brightness/fading control, a transistor is needed. N-channel MOSFET is very good for that.
The length of the strip and how much current it needs will determine the size of the transistor needed. AOI514 from digikey.com is inexpensive (50 cents), can control quite a few amps, and can be driven from Arduino directly.
AOI514 Alpha & Omega Semiconductor Inc. | Discrete Semiconductor Products | DigiKey
On/Off as fast as possible! 
I dont have a AOI514 but I have this:
- TIP120 NPN Darlington Transistor
- IRF520N HEXFET Power MOSFET IRF520
- LM7812 Voltage Regulator
- IRL540N Logic-Level HEXFET
- LM7809 Voltage Regulator
- IRF830 Power MOSFET
Can I use any of theese?
I have sent you a PM as well.