SSN

Luckily, you do not need much to request the Social Security Card.

First, you have to fill in a form, which you can fill once at the office while waiting to be called, or bring it filled from home.
Second, you need a document that proves where you were born. I brought both my Green Card and my Spanish birth certificate together with the official translation. It ended up being that with the Green Card it was enough. 
Lastly, but not least, the passport (any nationality).

NOTE: Instead of the Green Card you can use the Employment Authorization / Advance Parole Card. That way you may get your SSN before your Green Card! 

The office normally opens its doors about 30 minutes before the official opening, so you can go and get a number. Be ready to wait, depending on how busy it is you may be there a long time, or not.

The number of the Social Security Card will be assigned a couple of days after you apply, and the card itself will take about 2 weeks to make it to your house. In case you want to know your number (which you may need for a job contract or to register in university classes), you will need to go back to the office and wait on line (they do not give it to you through the phone). However, if you do not need to know it, just wait until it gets to your house!

Well, I hope this was helpful!