My wife showed her US visa stamp in her passport to the immigration official at the airport, and then handed over her visa packet from the US Embassy (we brought the required chest x-ray from the doctor in Malaysia who told us immigration may require it upon entering the US, but immigration never asked for it). The official brought us back to the office, where he took fingerprints of my wife and had her sign a couple of forms. He stated that she would receive her green card within 6 months, mailed to our address in the US. And finally, he provided a form for my wife to submit to a social security office in order to apply for a social security number.
A few days after our arrival, we drove to the nearest social security office and applied for a social security number. To apply, we completed a simple form at the office, handed over the form that we received from the airport immigration official, and showed my wife's passport. About a week later, my wife received her social security card in the mail, allowing her to start work immediately.
The green card arrived about a month after our arrival. It shows an expiration date of two years from now. I haven't looked into the details yet, but I believe we need to make some sort of declaration/confirmation of permanent residence about 90 days before the expiration of the card.
[FINAL UPDATE IN MAY 2016: I hope this blog has helped you with your own application! I'm sorry, I won't be able to answer comments or emails any longer. It's been almost 5 years since I went through the process, so I wouldn't want to provide any incorrect information to you. I'm sure some details on this blog will still be relevant, but since it was written in 2011, there must have been many updates to the process since then. Therefore, please check the USCIS website, and more recent forums for current information. All the best to you and your family!]