Build Truth Table given Circuit
You just need to put values on the inputs and go through the gates with calculation of result on each step (after each gate). And you should put on the input all possible values (as shown in your truth table draft)

For example:

if x1 = 0; x2 = 0; x3 = 0; then 
    A = 0 and 1 and 0 = 0; 
    B = 1 and 0 and 0 = 0; 
    F = 0 or 0 = 0;


So, thereby F = 0; when x1 = 0; x2 = 0; x3 = 0;

Next:

if x1 = 0; x2 = 0; x3 = 1; then 
    A = 0 and 1 and 1 = 0; 
    B = 1 and 1 and 1 = 1; 
    F = 0 or 1 = 1;


F = 1; when x1 = 0; x2 = 0; x3 = 1;

And so on to the end.

Update:

Completed truth table of the scheme:

X1 | X2 | X3 |  F
---|----|----|-----
0  | 0  | 0  |   0
0  | 0  | 1  |   1
0  | 1  | 0  |   0
0  | 1  | 1  |   0
1  | 0  | 0  |   0
1  | 0  | 1  |   1
1  | 1  | 0  |   0
1  | 1  | 1  |   0