Hi there,
I applied for my number 2 years after I starting working..mainly because my company told me they secured the number for me when in fact they crossed my record with someone else's so my number wasn't mine afterall! Anyway...I had my interview last spring and had to show proof of address (tenancy agreement and utility bill with my name and address), and proof of employment (my contract and pay slips) as I had been working, but as Peedal said you can secure a number before you start working. They also wanted bank statements and proof of income. As the others said, the form is actually completed during your interview and they asked all sorts of questions...they even rang me two days after my interview to ask about a stamp on my passport (I'd recently been to the US and they wanted to know for how long).
Anyway...an important caution for you: my company originally put me in the 'emergency' tax code because I didn't have a number, and this meant I got a temporary number and paid extra tax, which I then had to get that back. That being said, I'd try to get the number first so that you can give it to your employer once you are hired.
The forms on the website will give you all the info, and included is a check list of what to bring to your interview. In London the location of the Jobs centre you go to depends on your passport--they gave me the location when I rang them up.
Good luck!
Elizabeth