To request bitcoin from someone else they need your 'receiving address'. You can get your receiving address by choosing the 'Trade | Request Bitcoin' menu option or pressing the 'Request' tab.
To copy your receiving address to the system clipboard press the 'Copy' button. You can then paste the address directly into an email, Skype message etc to give it to the person sending you bitcoins.
You can also copy the QR code generated by pressing the 'Copy' button in the right hand side panel. You can then send the QR code to the payer by email, Skype etc.
You can also drag the QR code directly to your desktop and a PNG image file of the QR code is created.
You can have as many receiving addresses as you like. A typical usage is to have a different receiving address for each person that is sending you bitcoin so that you can tell them apart. You can create new receiving addresses by clicking on the 'New' button on the 'Request' tab.
In the 'Label' field you can add a label to the receiving address to help you remember who is sending you bitcoin.