The Arduino (or other 5 Volt microcontroller) can be powered off the same supply as the LED strip, by splitting the power leads (after the diode, if used) and connecting to the Arduino’s 5V pin (not Vin) and GND.

LED strips aren’t picky about which side they receive power from, only data. In a pinch, if the situation really calls for it, you can connect the battery pack (with diode, if used) to the OUT end of the strip, then power the Arduino from the + and – connections on the IN end (along with the serial data and clock signals). This isn’t recommended though, because voltage drops slightly along the length of the strip, and the Arduino (which is supposed to be running everything) will give out sooner as the batteries approach depletion. Powering the Arduino close to the batteries ensures a healthy voltage, to stay in control for as long as possible.