Find an Arduino sketch that configures for serial data by creating 'clock', 'data' and 'latch' lines. Such configurations are often used for shift-register applications like message board controls (scrolling text displays). Alternatively program three i/o pins yourself and 'bit-bang' the signal.
i.e. Load the respective register(s) with data according to the settings for the device you wish to control and according to the data sheet page 5. Start with an 'all-off' signal to guarantee a known switch-on state for the gates and prevent spurious power-up events.
Send the data/clock/sync as required...... (serially shift your data to the data pin, increment your clock, repeat until all data is out then send a sync pulse).
The analogue switch device isn't bi-directional (data-wise) so you can't monitor the status of the switches other than by checking that their outputs are working by some other means.