In past years, people applying to adjust status (get a green card) from within the U.S. could submit their adjustment of status packet to a local District Office of U.S. Citizenship and Immigration Services (USCIS, formerly called INS). Newer procedures, however, require you to send it to a designated office called a “lockbox.” USCIS made this change in hopes of speeding up the handling of applications. Your interview, however, will be handled by your local USCIS district office.
After you have prepared all your paperwork--including Forms I-130 (if you haven't already gotten one approved by USCIS), I-485 (the main application for a green card), I-765 (for a work permit), I-131 (for an Advance Parole travel document), G-325 (biographical information), I-693 (medical exam results; though you might want to wait to submit this), and other forms and documents as required depending on what category you are applying in--make a complete copy of every form, document, photo, and check or money order in your packet, for your records. (Government agencies have a tendency to lose things, and you may be called upon to prove that you actually submitted something.)
Then send the packet to the address listed on the I-485 page of the USCIS website. Notice that the address is slightly different if you use a courier service (like FedEx) rather than the U.S. Postal Service. Whatever service you use, make sure to ask for a return receipt or certified mail, so that you will have proof that it got there.
Once USCIS has received and accepted your adjustment of status packet for processing, it will put you on the waiting list for an interview. The agency will send you paper receipt notices--one for your I-485, and one each for your I-130, I-765, and I-131, if you filed those applications at the same time. (See the sample receipt below.) The receipt is a very important document. Make several photocopies and store them in secure places.
Among other things, the receipt will contain the immigrant's A-number, which you will need if you have to correspond with USCIS about your case. (USCIS is a big bureaucracy: Your number will now become more important than your name.)
Soon after getting your receipt(s) you should receive an Application Support Center (ASC) Appointment Notice. The notice schedules you for a biometrics appointment to have your fingerprints, photo, and signature taken. The photo and signature are used to create your work permit and your Advance Parole travel document, if you requested those. Your fingerprints are taken for processing your application for adjustment of status.
The work permit is good for one year. Once your case is approved and you become a permanent resident, you no longer need a work permit. Your right to work is evidenced by your permanent resident card. In case your application is delayed for some reason, however, you can renew the work permit for one-year periods for as long as you are waiting for a decision on your adjustment of status application.
Finally, you will be called in for an interview at your local USCIS office. Your green card should, if all goes well, be approved at this interview or soon after.