You don't mention if you are using and Arduino, but I will assume that is the case.
Using the shift register to light up LEDs is fairly straight forward.
You can use the ShiftOut() function to send out an 8bit binary value to the register. https://www.arduino.cc/en/Reference/ShiftOut
In summary however, if you want to light up the LEDs on the output pins 2 and 7 you would shift out b01000010 to the shift register. If you wanted pins 4, 5 and 7 to light up, you shift out b01011000. These assume the least significant bit is sent first.
Here's an example:
// set shift register output pins 2 and 7 to high
uint8_t data = 1<<2 | 1<<7; // use bit shifting
shiftOut(dataPin, clockPin, LSBFIRST, data); // send the data