How to get a simplified circuit out of three smaller circuits

I'm not going to tell you too much; you show too little of your own efforts. Just a few basic tips to get you started.

You'll have to start with the truth table. With 3 inputs you have only 8 combinations. Start without the borrow bit (the half of the table for which it's zero). Then subtracting shouldn't be too hard: what's the result if you subtract 0 from 1? Or 1 from 1? If you want to introduce the borrow bit it could be useful to do the subtraction of two decimal numbers, that should be familiar since elementary school. Observe how the result is different with or without borrow. Keep it simple: 25 - 13 is without borrow, 25-17 is with borrow. That should get you started.

The best way to do this is to analyze each case separately. This gate has two input signals, so only four combinations to analyze. For each case write down the inputs and the resulting output. After the four cases, you have a truth table, which you say you already understand.

Here is the case with both inputs 0:

Both transistors are obviously off, so the pullup drives the output high.

Now do the (1,0) inputs case:

The bottom transistor is obviously off, so again the outut can only be high.

Case (0,1):

Case (1,1):

From these four cases you get the truth table:

  In1  In2  Out
  ---  ---  ---
    0    0    1
    1    0    1
    0    1    1
    1    1    0

which is the NAND function.