Dealing with power issues when controlling LED strip with Arduino

Hey Folks, I'm trying to use a flowmeter to control an LED strip and I've read on a few different pages that the Arduino's supply voltage is too limited to connect the LED to it. I purchased a power adapter for the LED strip (Supernight SMD 5050) and I was wondering if I can somehow use the power adapter (so as to avoid using Op-Amps or transistors and simplify the system) while still using the Arduino to control the output? Clearly I'm not the most experienced with electronics, so any help would be greatly appreciated!

Thanks!