A simple Arduino is not enough. However you only need to attach a motor shield to it and connect it to your computer over USB. A couple of jumper wires are also needed to create this connection (as per the manual here).

You need a separate power supply to connect to your motor shield (make sure your break the connection between the input voltage and Arduino on the motor shield). A laptop one (19V) is fine. 12V should also do, if you happen to have a wireless router (or similar) 12V, 1A around it will do in a pinch. And they usually have Arduino-compatible 5.5mm barrel plug, so one worry less.

Write DCC++ BaseStation to your Arduino board, install JMRI on your computer and you are ready to program CVs, run trains or create any complicated scenario you can think of.

That said, your decoders must be DCC-aware. Most are, but if you have older Marklin ones they might not be. That's the only exception that I found so far, any other brand is a priori ok.