I want to know how this circuit of NAND gate work and the direction of current in each wire in the circuits

 

Have you tried this in a circuit simulator? I guarantee that it will answer your questions...

 

I want to know how this circuit work

 

What is your understanding of electronics?

Understanding how the circuits works is different from understanding what it is doing.

 

What is your understanding of electronics?

Understanding how the circuits works is different from understanding what it is doing.

I can't understand the the transistor Q1 with representation with diodes

 

There are three possible combination of inputs. Both HI (equal to Vcc), both LO (equal to ground), and mixed (one HI and the other LO).

Take each combination in turn and decide which diodes are ON and which diodes are OFF. Make a table and post that to give us something to start with.

If you need to study up on diodes, check out Vol 3 of the E-book

http://www.allaboutcircuits.com/vol_3/index.html