The correct answer depends on the impedance of the device you want to control.
One way is to integrate the 5volt PWM first with a resistor and a capacitor.
Followed by a 2.4x amplifying opamp.
This won't "load" the integrator, so good linearity.
Another way is to first amplify the 5volt PWM to 12volt PWM with a transistor.
And then integrate the 12volt PWM.
Works only if the device is not "loading" the output voltage.
You need 3 NPN transistors.
Arduino drives base of each thru a 220, 250, 270 resistor, something in that range (but no less than 220).
Emitters connect to Gnd.
Collectors connect to R, G, B of LED strip, + to 12V.
analogWrite the values you want control brightness of each color.
Each 3 LEDs in the strip will require about 60mA. How many LEDs in the strip you are using? That will have an impact o the transistor you use, and perhaps change to N-Channel MOSFET might be suggested, such as AOI514: http://www.digikey.com/product-search/en?vendor=0&keywords=aoi514
Yes, that will work and is the easiest and most common way. That's why it has a configuration like that. Controlling a 12V led strip with an Arduino is done like a million times before so yeay....