How to obtain new "2-step verification" passwords from Gmail and for each PC or Laptop.
First , you need to open the "account" settings within the Google Mail  interface and select "Security". Scroll down to How you sign-in to Google. See picture hereafter.
Within that screen , you need to turn on the "2-Step Verification"  (1) . Afterwards , you need to push the ">" arrow at the right (2)   Do not panic when Google ask you to login again with your classic password. This will happen several times.
Up to the step now after pushing (2) .... Scroll down till you see the picture hereafter.
You now see a "App passwords" screen. Click on the ">" arrow.
Up to the next picture ....
I presume that you do not have passwords saved yet , so their will be no entries to show. 
Fill in a name of your choice , for example your name or whatever at "App name"
Up to the next picture ....
As you may have seen from within the pictures , I used the name of my computers as they appear on my internal network.  You will need to create a separate password for each PC , and you will have to generate those passwords on the specific PC's themselves. You can not generate a password for a particular PC on another PC.  Now , push the "Create button.
Up to the next picture ....
You will now been offered with the "2-step verification" password. You can note this down , or  ....
I always highlighted the password and copied it into the Clipboard.  If you paste this password into , for example an email , you get it displayed as hereafter , but that is NOT what you want to use !  
You must paste the password into Notepad , and then you will see it without the spaces between the signs , thus this irhiccrlrlgdywgq  . This is the form that you will have to enter into the password settings of Outlook Express. Save the password from within Notepad for later use.
Finally , up to the last picture ...
You will now see that a new password "AMDK7"  has been generated.  You may delete at any time the password via the black trash icon at the right. During this procedure , you will also receive "security alert" emails from Google. You need to push the "Check Activity" button within them , and then acknowledge them with "Yes , it's me"

How to configure a Gmail account in Outlook Express.

One may create an account within Outlook Express , but this will hardly be complete and will certainly not be usable with Gmail. Next pictures show the account settings which need to be changed and that at least worked for me. ( The "" address is fake )

The "General" tab

The "Servers" tab

No need to mention that you have to fill in your 2-step verification password.

At the bottom of the "Servers" tab , you need to press the "Settings" button. A new window will pop up where you need to fill in your email adress and your 2-step verification password as well.

The "Advanced" tab

The other tabs do not need to be changed.