Your mainboard (Asus Z97-K) does not have an Aura RGB header, which means you cannot connect the LEDs directly to the mainboard, you need a controller where you can connect the LEDs so that you can change the colours.
You need something like: NZXT HUE+ RGB LED Controller (RGB, 40, 300mm)

Connecting them should actually work with practically any mainboard, as they are simply plugged in with a 4-pin connector. However, this alone won't do you much good, because you need an "Aura" capable mainboard to be able to use the different colours. Your board doesn't look like it has this feature, but I only had a quick cursory look.
Of course, the easiest way would be to have a Phanteks case with an integrated controller ;)

The coloured LEDs need a controller that takes over the colour selection. At Asus it is called "AURA". My ASUS Z270G strix has two 4-pin connectors with round pins. So I needed the following additional adapter cable:Art-Nr 5839037 (listed in the accessories), because the connector of the LED strip is designed for square pins. I couldn't find an AURA connector in the description of your board (Asus Z97-K). Just have a look at the ASUS page...