Build a temperature monitor by using One 2-digit LED and one Shift Register

I'm new to Arduino. I have to build a temperature monitor by using
Shift Register.
A 2-digit LED(LDD-HTF304NI).http://datasheet.octopart.com/LDD-HTF304NI-Lumex-datasheet-13230160.pdf
Two buttons.
Temperature sensor.

The behaviour of the system should be:

In the default state, the temperature is displayed on the display.

When button 1 is pressed: the system records ten temperatures at one-second intervals, with some form of indication to show that it is gathering data. When data collection ends, the system should return to the default state, and give some form of indication that it has done so. The temperatures recorded should be stored for later use.

When button 2 is pressed, either:
If there are stored temperatures in memory, the system displays them.
If there are no stored temperatures in memory, the system indicates this.

Can someone give me some advice about the code, please?

You should know about debouncing switches, 7 segment digit encoding, multiplexed display, and state machines. Write subroutines for these tasks, which you call from the state switch in loop().

For driving the display you also need two drivers (FET...), for switching between the digits.