Let's get through the legal stuff. In the United States, a Social Security number (SSN) is a nine-digit number issued to U.S. citizens, permanent residents, legal immigrants and temporary (working) residents under section 205(c)(2) of the Social Security Act, codified as 42 U.S.C. § 405(c)(2). The number is issued to an individual by the Social Security Administration, an independent agency of the United States government. Its primary purpose is to track individuals for taxation purposes.

As a K-1 Visa Holder you are eligible to receive a SSN upon producing a valid I-94 (unexpired). Do not wait until you only have a few weeks left until your I-94 expires to file for a SSN. Many SSA (Social Security Administration) offices will not allow you to file for a SSN if your I-94 is about to expire (generally 14 days prior to the expiration on your I-94). On the other hand, you should also not file for a SSN too soon either.

You should wait 2 weeks after you arrived in the US before applying for a SSN. UPDATE: It's been reported recently that you no longer need to wait 2 weeks till you are in the SAVE database that you can go the next business day. If you go too soon your record of arrival will not be in the SAVE-ASVI system yet (what is SAVE), and it will require manual verification from the USCIS. As this will add weeks to the period it takes to process the SSN, it is advisable to attempt to wait the two weeks to be safe. If you have waited the 2 weeks and they tell you they cannot verify your arrival record via the SAVE database, then personally return on another day to have them search again -- thus eliminating the manual verification (you don't want to do the manual verification as it adds so much more time to the process).

To apply for a SSN you will need to go to your local SSA office and bring the documents below. These documents are proof of your eligibility to file for a SSN:
 

1. The SS-5 form  download and complete the application (they have some at the office if you forget).

2. Your Passport (with the K-1 Visa attached)

3. Your valid I-94

4. Another form of valid ID (birth certificate will do nicely)

5. You should also print and bring the document RM 10211.530 , in the event that the agent is not knowledgeable that K-1/K-2 are eligible to receive a SSN.

Make sure to bring all the documents above because some offices have staff that are not aware that a K-1 Visa Holder is eligible to file for a SSN. A friendly reminder is a nice thing to have -- if not you could be turned away incorrectly.

Once you have successfully applied for your SSN, the SSN card will come in the mail in about 2 weeks.

K2 visa holders must first have a work permit (EAD) to get a social security number.

After marriage

Carry your marriage certificate to the social security office to get the social security card in the new name. If you applied for a social security number before marriage, you can go back to the social security office after marriage and get your name changed on your social security card.

The social security card will be marked “VALID FOR WORK ONLY WITH USCIS AUTHORIZATION”.  That means, you need to get your EAD first before you can actually work.  Hopefully, when you submitted your AOS you included the EAD. If not you will now need to sumit the paperwork for an EAD prior to working.