Ah, so my shift registers are different to the normal ones? Drat...
No drat.... needed!
This shift register with output latches is actually better than one without output latches! Without the latches the LED's will display all the random patters that "flow by", while you clock data in.
Its an 8-bit device, so if you need 20 outputs you need 3 of them.
shift and latch clocks can be tied in parallel, and clear input SRCLR can be tied inactive, (high) and output enable OE can be tied permanently low.
QH' outputs from one shift register, should be connected to the SER input of the next shift register to "chain" the three chips together.
First start with setting SET low as well as RCLK.
now you can begin:
Place data on the first chips SET input then clock SRCLK high then low again
Now you have pushed one bit, (for the last LED in the chain) into the shift register.
Do the same for the next 19 bits.
Now drive RCLK high and low again to latch the data in the shift register into the latches. The right bits will appear on the outputs (you can simply ignore the last 4 outputs).
now "rinse and repeat".
If you want to manipulate individual bits, use an array of bits, holding 20 bits. Manipulate the bit(s) you want to change in that array, then write the whole array to the latches.
Don't forget to put resistors in series with each LED, something like 220 Ohm should work.