There are LED Strips with just a 12V supply as already mentioned and all you can do is turn them on and off, or dim them with a Pulse width modulated On Off. These strips can take a fairly large current (e.g 1.2A per metre) so I would be looking at a HexFet to turn them on and off, if you wanted to handle more than 0.5 metre. Devices like IRF3205 have very low on resistance and could easily handle a 5metre strip. You do want to drive the HexFet gate fairly hard (>8V) so you could use one of the open collector outputs on the Gertboard with a pull up resistor to the 12V line.
The second sort of LED strip, which is more interesting, is where each pixel in the strip has its own control and you drive values down a serial bus to control the intensity and color of each pixel in the strip. The SPI serial from the RPI is ideal for this as you need to send quite a lot of values quickly to get dynamic control of all the pixels. This is the sort of method used by Boblight to give ambient lighting around a TV based on the video.