The clock and data pins are for your serial input. These can be controlled directly from the Arduino, just connect each to a digital out.  

For the data routine, according to the datasheet there is one start bit, followed by 35 data bits which correspond to the "Serial Input Sequence" table in your question.

Create a function in your "sketch" to control the serial loading, something like below - I haven't checked this code.  
You will have to replace the `set_data_pin` and `set_clock_pin` with the correct Arduino calls to whatever GPIO pins you have attached to the clock data pins on the display (I don't use Arduino so I don't know them) Same for the `delay_us` (microsecond delay) which can be adjusted to whatever timing you want up to 500kHz clock speed - you can add a define for the value to save changing each one.  
Each segment is shifted out MSB to LSB, which corresponds with A(MSB) to DP(LSB) for each input char: 

    void load_data(char seg1, char seg2, char seg3)
    {
        char i, temp;
        char position = 0;
    
        set_data_pin(1);  // clock start bit in
        set_clock_pin(1);
        delay_us(5);
        set_clock_pin(0);
    
        temp = seg1;
        while(i<8)
        {
            set_data_pin(temp & 0x80);  // set data pin
            set_clock_pin(1);
            delay_us(5);
            set_clock_pin(0);
            i++;
            temp = temp << i; // shift next bit out
        }
        
        temp = seg2;
        while(i<8)
        {
            set_data_pin(temp & 0x80);  // set data pin
            set_clock_pin(1);
            delay_us(5);
            set_clock_pin(0);
            i++;
            temp = temp << i; // shift next bit out
        }
     
        temp = seg3;
        while(i<8)
        {
            set_data_pin(temp & 0x80);  // set data pin
            set_clock_pin(1);
            delay_us(5);
            set_clock_pin(0);
            i++;
            temp = temp << i; // shift next bit out
        }
    
        // Last 11 bits - do something here if needed
        while(i<11)
        {
            set_data_pin(0);  // set data pin
            set_clock_pin(1);
            delay_us(5);
            set_clock_pin(0);
            i++;
        }
    }