1st you'lll need the hardware (µC, clock oszillator LCD, butttons etc.).
2nd you'lll need a counter for the time which is clocked in 1 second intervalls, e.g. by an interrupt.
You'll need a register to store the alarm time
You'll need a display routine to display the time on the LCD. This routine will have to update the display anytime it changes.
You'll need a routine that reads the button states (don't forget to de-bounce the buttons).
Depending on the button states (user actions) you'll have to increment or decrement the clock counter to allow setting of the time. Likewise you'll have to increment or decrement the alarm counter.
Your display routine could display clock and alarm at the same time since you have a 2-row LCD.