Hallo Konstantinos,

may be I'm overlooking something, but this task is very easy! Serial interfacing is often done in a very simple way: First you put your data to some output port. Then, a little bit later, when data has stabilized you make at a second output port a 0-to-1 transition or 1-to-0-transition (depends on actual interface specification). With this transition data is latched in your device.
Sometimes a third line is used, for enabling your device. This arrangement is called '3-wire serial interface'.
There are several standards arround, 'microwire', 'SPI', 'QSPI', etc. Have a look at datasheet of your digital potentiometer, what kind of standard it accepts. There, you will also find specifications of serial interface. So, you can't make anything wrong...

Good luck,
Kai